# Posts by Tags

- 04.65.+e 8
- 04.70.-s 1
- 1/n expansion 6
- 11.15.-q 3
- 11.15.bt 9
- 11.25.-w 1
- 11.25.db 2
- 11.30.pb 5
- 11.55.-m 1
- 11.55.bq 6
- 12.10.-g 1
- 12.38.bx 4
- 12.60.jv 2
- BCFW 1
- BCFW Mathematica tutorial 1
- BCFW bridge 1
- BCJ 7
- BCJ relations 1
- CHY 1
- Compton amplitudes 1
- Feynman integrals 2
- Feynman parameters 1
- GKP string 1
- Goncharov 1
- Graham determinants 1
- Grassmannian 1
- Hopf algebra 1
- IBP relations 1
- IBPs 1
- IR safety 1
- KLT 2
- LHC 1
- Lax representation 1
- Lee-Pomeransky 1
- Liouville theorem 1
- Lyndon basis 1
- MHV 2
- MZV 1
- Monte Carlo 1
- Multiple Polylogs 1
- N=2 superQCD 2
- N=4 SG 1
- N=4 SYM 6
- N=8 SG 2
- Neumann model 1
- PARI 1
- PSLQ 1
- Periods 1
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- QCD phenomenology 1
- QED vertex renormalization 1
- RNS worldsheet action 1
- S matrix 1
- SAGEX 12
- Schwinger parameters 1
- Shuffle algebra 2
- Shuffle identities 1
- Superconformal symmetry 1
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## 04.65.+e

- » Black holes in N=8 supergravity from SO(4,4) hidden symmetries
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
- » Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops

## 04.70.-s

## 1/n expansion

- » Building Bases of Loop Integrands
- » How tropical are seven- and eight-particle amplitudes?
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » The Double Pentaladder Integral to All Orders
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

## 11.15.-q

- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand
- » Towards a Basis for Planar Two-Loop Integrals

## 11.15.bt

- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
- » D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand
- » Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops
- » Towards a Basis for Planar Two-Loop Integrals

## 11.25.-w

## 11.25.db

- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops

## 11.30.pb

- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
- » D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
- » Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes

## 11.55.-m

## 11.55.bq

- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
- » D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand

## 12.10.-g

## 12.38.bx

- » Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory
- » Analytic result for a two-loop five-particle amplitude
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » Towards a Basis for Planar Two-Loop Integrals

## 12.60.jv

- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops

## BCFW

## BCFW Mathematica tutorial

## BCFW bridge

## BCJ

- » Extracting Einstein from the Loop-Level Double-Copy
- » Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
- » All Summer School Lectures for Amplitudes 2018
- » N=4 SYM and N=8 SG 5-loop integrands
- » Amplitudes related Graph Tools
- » All Summer School Lectures for Amplitudes 2017
- » Two-loop supersymmetric QCD and half-maximal supergravity integrands

## BCJ relations

## CHY

## Compton amplitudes

## Feynman integrals

- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Lectures for the first SAGEX scientific School (DESY)

## Feynman parameters

## GKP string

## Goncharov

## Graham determinants

## Grassmannian

## Hopf algebra

## IBP relations

## IBPs

## IR safety

## KLT

- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Lectures for the first SAGEX scientific School (DESY)

## LHC

## Lax representation

## Lee-Pomeransky

## Liouville theorem

## Lyndon basis

## MHV

- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Lectures for the first SAGEX scientific School (DESY)

## MZV

## Monte Carlo

## Multiple Polylogs

## N=2 superQCD

- » Integrated One and Two Loop Four-Point Super-QCD
- » Two-loop supersymmetric QCD and half-maximal supergravity integrands

## N=4 SG

## N=4 SYM

- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Lectures for the first SAGEX scientific School (DESY)
- » Converting from Schnetz f-alphabet to MZVs through weight 14
- » Six-Gluon Amplitudes in Planar N=4 Super-Yang-Mills Theory at Six and Seven Loops
- » N=4 SYM and N=8 SG 5-loop integrands
- » Bourjaily -- Mathematica for N=4 Tree Amplitudes

## N=8 SG

## Neumann model

## PARI

## PSLQ

## Periods

## Polylogarithms

## QCD phenomenology

## QED vertex renormalization

## RNS worldsheet action

## S matrix

## SAGEX

- » Scattering amplitudes and form factors in EFT
- » Geometrical aspects of amplitudes and correlators in N=4 SYM
- » Classical Gravity from Gluon Interactions
- » On-shell techniques for Effective Field Theories
- » Massive 2- and 3-loop corrections to hard scattering processes in QCD
- » Perturbative integrability in 1+1 dimensions and affine Toda theories
- » Multipoint conformal blocks in conformal field theories
- » Non-planar anomalous dimensions in sYM theories
- » Coherent states and classical radiative observables in the S-matrix formalism
- » Unitarity approaches to two-loop all-plus amplitudes
- » The On-Shell Highway To Waveforms
- » Heavy particles and the binary inspiral problem

## Schwinger parameters

## Shuffle algebra

- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Lectures for the first SAGEX scientific School (DESY)

## Shuffle identities

## Superconformal symmetry

## Symbols

## Z-theory

## abelian

## abjm

## abjm model

## ads(5) x s(5)

## ads/cft correspondence

## algebra

- » Planar two-loop integrals for $mathbf{μe}$ scattering in QED with finite lepton masses
- » The Two-Loop Four-Graviton Scattering Amplitudes
- » The Double Pentaladder Integral to All Orders

## algebra cluster

- » Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
- » How tropical are seven- and eight-particle amplitudes?
- » Cluster patterns in Landau and Leading Singularities via the Amplituhedron
- » Algebraic singularities of scattering amplitudes from tropical geometry
- » Cluster adjacency properties of scattering amplitudes
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes

## algebra hopf

## algebraic geometry

## alphabet

## amplitude analysis

- » One-loop matrix elements of effective superstring interactions: $α'$-expanding loop integrands
- » Manifestly Dual-Conformal Loop Integration
- » The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy

## amplitudes

- » SAGEX 2021 PhD Organized Summer School
- » SAGEX Mathematica and Maple School Lectures
- » Integrated One and Two Loop Four-Point Super-QCD
- » Six-Gluon Amplitudes in Planar N=4 Super-Yang-Mills Theory at Six and Seven Loops
- » The two-loop five-point amplitude in N=8 supergravity
- » All Summer School Lectures for Amplitudes 2018
- » Amplitudes related Graph Tools
- » All Summer School Lectures for Amplitudes 2017

## amplitudes meet experiment

## analytic continuation

## analytic properties

- » Soft gluon emission at two loops in full color
- » Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops
- » Cluster adjacency properties of scattering amplitudes

## angular momentum

## anomalous dimension

- » Four-loop collinear anomalous dimensions in QCD and $mathcal{N} = 4$ super Yang-Mills
- » Cosmic Wheels: From integrability to the Galois coaction
- » Structure of two-loop SMEFT anomalous dimensions via on-shell methods
- » The Origin of the Six-Gluon Amplitude in Planar $mathcal{N}=4$ SYM
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
- » Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory

## anomaly u(1)

## any-dimensional

- » SUSY in the Sky with Gravitons
- » Local integrands for two-loop all-plus Yang-Mills amplitudes
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Double-Copy Constructions and Unitarity Cuts

## approximation classical

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Extracting Einstein from the Loop-Level Double-Copy
- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams

## approximation eikonal

## astro-ph

## axial-vector

- » The axial-vector contributions in two-photon reactions: pion transition form factor and deeply-virtual Compton scattering at NNLO in QCD
- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD

## axion

## b1(1235) mass

## background schwarzschild

## bcj relations

## belle

## bethe ansatz

## beyond standard model

## bfkl equation

- » Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $mathcal{N} = 4$ Super Yang-Mills and $mathcal{N} = 8$ Supergravity
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Bootstrapping the three-loop hexagon

## bhabha scattering

## binary

- » Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
- » Scattering Amplitudes and Conservative Binary Dynamics at ${cal O}(G^4)$
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes

## binary compact

- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
- » Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory

## binding energy

- » Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics

## black hole

## black hole angular momentum

## black hole binary

- » Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
- » Tidal Effects in the Post-Minkowskian Expansion
- » Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory

## black hole dyon

## black hole kerr

## black hole scattering

- » Extracting Einstein from the Loop-Level Double-Copy
- » Radiative Classical Gravitational Observables at $mathcal O(G^3)$ from Scattering Amplitudes

## black hole spin

## black holes

- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory

## bootstrap

- » Extracting Einstein from the Loop-Level Double-Copy
- » A Three-Point Form Factor Through Five Loops
- » The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
- » Bootstrapping an NMHV amplitude through three loops

## born-infeld model

- » Covariant Color-Kinematics Duality
- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Hidden Supersymmetry May Imply Duality Invariance

## bosonic strings

- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » Inverse of the String Theory KLT Kernel

## boundary condition

- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
- » On the Renormalization of the Effective Field Theory of Large Scale Structures

## bps

## bremsstrahlung

## bubble

## buildings

- » Simple encoding of higher derivative gauge and gravity counterterms
- » Building Bases of Loop Integrands
- » Positivity Sectors and the Amplituhedron

## calorimetry

## capture

## celestial amplitudes

## cern lab

## cern lhc coll

- » The $ppto W(to lν)+γ$ process at next-to-next-to-leading order
- » Constructing d-log integrands and computing master integrals for three-loop four-particle scattering

## charge coulomb

## charge electric

## charge magnetic

## charge nut

## chern-simons theories

## chiral

## chiral lagrangians

## chiral-multiplets

## classical black-hole scattering

## classical theories of gravity

- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
- » Extremal black hole scattering at O(G^3): graviton dominance, eikonal exponentiation, and differential equations
- » Unitarization from Geometry
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory
- » Gravitational Radiation from Color-Kinematics Duality

## cluster

- » The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory

## cluster algebras

## collinear

- » Four-loop collinear anomalous dimensions in QCD and $mathcal{N} = 4$ super Yang-Mills
- » Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
- » Soft gluon emission at two loops in full color
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

## collinear limits

## color

- » Covariant Color-Kinematics Duality
- » Composing Effective Prediction at Five Points
- » Double copy for massive quantum particles with spin
- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » Amplitudes at Infinity
- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
- » Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops
- » The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
- » Berends-Giele recursion for double-color-ordered amplitudes
- » Color-Kinematics Duality for QCD Amplitudes
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Double-Copy Constructions and Unitarity Cuts
- » Recursion in multiplet bases for tree-level MHV gluon amplitudes
- » Decomposing color structure into multiplet bases
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
- » Orthogonal multiplet bases in SU(Nc) color space

## color dependence

## color kinematics duality

## color ordered

## color su(n)

## color-kinematic duality

## colored particle

## compactification

## compass

## computer algebra

## conformal

- » Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
- » Hexagon functions and the three-loop remainder function
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory

## conformal and w symmetry

## conformal symmetry

## conservation law

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Scattering Amplitudes and Conservative Binary Dynamics at ${cal O}(G^4)$
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Tidal Effects in the Post-Minkowskian Expansion
- » Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory

## convergence conditions

## correction finite size

- » SUSY in the Sky with Gravitons
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
- » Tidal Effects in the Post-Minkowskian Expansion

## correlation function

- » One-loop matrix elements of effective superstring interactions: $α'$-expanding loop integrands
- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

## correlation functions

## coset space

- » Black holes in N=8 supergravity from SO(4,4) hidden symmetries
- » N=4 conformal supergravity: the complete actions

## cosmic flows

## cosmic web

## coupling constant

## coupling linear

## coupling minimal

## coupling nonminimal

## covariance

- » Covariant Color-Kinematics Duality
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics

## cross section

## cross section ratio

## curvature tensor

## cuts

## data analysis method

## deep inelastic scattering

## deeply virtual compton scattering

## deflection

## deformation

- » Tidal Effects in the Post-Minkowskian Expansion
- » Hidden Supersymmetry May Imply Duality Invariance

## density

## derivative high

- » Composing Effective Prediction at Five Points
- » Simple encoding of higher derivative gauge and gravity counterterms
- » Mining the Geodesic Equation for Scattering Data
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string

## differential and algebraic geometry

- » Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
- » Algebraic singularities of scattering amplitudes from tropical geometry
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory

## differential equations

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Analytic results for two-loop planar master integrals for Bhabha scattering
- » Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
- » Cosmic Wheels: From integrability to the Galois coaction
- » Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
- » Master integrals for the NNLO virtual corrections to $q bar{q} rightarrow t bar{t}$ scattering in QCD: the non-planar graphs
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals
- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs
- » The Double Pentaladder Integral to All Orders
- » Hexagon functions and the three-loop remainder function

## differential forms

## dijet production

## dilatation operator

## dilaton

## dimension 3

## dimension 4

- » Building Bases of Loop Integrands
- » Black holes in N=8 supergravity from SO(4,4) hidden symmetries
- » Ultraviolet Properties of N = 8 Supergravity at Five Loops
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops
- » Towards a Basis for Planar Two-Loop Integrals

## dimension 5

- » D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops

## dimension 6

- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
- » Towards a Basis for Planar Two-Loop Integrals

## dimension 8

- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » Towards a Basis for Planar Two-Loop Integrals

## dimensional reduction

## dimensional regularization

## dispersion

- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

## dispersion relation

- » Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
- » Dispersion relation for hadronic light-by-light scattering: pion pole

## dissipation

## distribution amplitude light cone

## double copy

- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Summer School Lectures for Amplitudes 2018
- » N=4 SYM and N=8 SG 5-loop integrands
- » Amplitudes related Graph Tools
- » All Summer School Lectures for Amplitudes 2017
- » Two-loop supersymmetric QCD and half-maximal supergravity integrands

## double field theory

## duality

- » Covariant Color-Kinematics Duality
- » Three-loop color-kinematics duality: 24-dimensional solution space induced by new generalized gauge transformations
- » Double copy for massive quantum particles with spin
- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » Manifestly Dual-Conformal Loop Integration
- » Amplitudes at Infinity
- » Gravitational Radiation from Color-Kinematics Duality
- » The Double Pentaladder Integral to All Orders
- » Interplay of colour kinematics duality and analytic calculation of multi-loop scattering amplitudes: one and two loops
- » Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Color-Kinematics Duality for QCD Amplitudes
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Double-Copy Constructions and Unitarity Cuts
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
- » Review of AdS/CFT Integrability: An Overview
- » Bootstrapping the three-loop hexagon

## duality in gauge field theories

- » Composing Effective Prediction at Five Points
- » Double copy for massive quantum particles with spin

## duality invariance

## duality violation

## dyon

## effective field theories

- » Composing Effective Prediction at Five Points
- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
- » Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $mathcal{N} = 4$ Super Yang-Mills and $mathcal{N} = 8$ Supergravity
- » Unitarization from Geometry
- » Structure of two-loop SMEFT anomalous dimensions via on-shell methods
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory
- » Dispersion relation for hadronic light-by-light scattering: pion pole
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » Berends-Giele recursion for double-color-ordered amplitudes

## effective field theory

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Standard Model EFTs via On-Shell Methods
- » Scattering Amplitudes and Conservative Binary Dynamics at ${cal O}(G^4)$
- » Composing Effective Prediction at Five Points
- » Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
- » Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $mathcal{N} = 4$ Super Yang-Mills and $mathcal{N} = 8$ Supergravity
- » Tidal Effects in the Post-Minkowskian Expansion
- » Structure of two-loop SMEFT anomalous dimensions via on-shell methods
- » Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
- » One-loop renormalization in Galileon effective field theory
- » One-loop renormalization in Galileon effective field theory
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
- » On the Renormalization of the Effective Field Theory of Large Scale Structures

## effective hamiltonian

## effective lagrangian

## efficiency

## eikonal

- » SUSY in the Sky with Gravitons
- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Radiative Classical Gravitational Observables at $mathcal O(G^3)$ from Scattering Amplitudes
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory

## einstein

- » The Two-Loop Four-Graviton Scattering Amplitudes
- » On the Renormalization of the Effective Field Theory of Large Scale Structures

## einstein-maxwell equation

## einstein-yang-mills theory

## elastic scattering

- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## electromagnetic field duality

## electron

- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## electron mass

## electron muon scattering

## electron muon to electron muon

- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## electron nucleon scattering

## electron positron elastic scattering

## electron positron to muon+ muon-

- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## electron positron to pi pi pi

## electroweak interaction correction

## elementary particles and fields

- » All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
- » Scattering Amplitudes and Conservative Binary Dynamics at ${cal O}(G^4)$
- » An Elliptic Yangian-Invariant, `Leading Singularity'
- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » Tidal Effects in the Post-Minkowskian Expansion
- » The Origin of the Six-Gluon Amplitude in Planar $mathcal{N}=4$ SYM
- » The Two-Loop Four-Graviton Scattering Amplitudes
- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » Analytic result for a two-loop five-particle amplitude
- » The two-loop five-point amplitude in $mathcal{N} =4$ super-Yang-Mills theory

## elliptic polylogarithms

## embedding

## energy flux

## energy loss

## energy low

## energy-momentum

## epsilon expansion

## error statistical

## euclidean

## excited state kaluza-klein

## expansion 1/n

## expansion 1/n color

## extended supersymmetry

- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » How tropical are seven- and eight-particle amplitudes?
- » N=4 conformal supergravity: the complete actions
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Bootstrapping an NMHV amplitude through three loops
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

## f-alphabet

## factorization

- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » Soft gluon emission at two loops in full color
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » All Lectures for the first SAGEX scientific School (DESY)
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Bootstrapping an NMHV amplitude through three loops
- » Hexagon functions and the three-loop remainder function

## factorization collinear

## fermion clover

## fermion massive

## fermion pair

## feynman

## feynman graph

- » Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
- » Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
- » Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics
- » Unitarization from Geometry
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » One-loop renormalization in Galileon effective field theory
- » The Two-Loop Four-Graviton Scattering Amplitudes
- » Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
- » Manifestly Dual-Conformal Loop Integration
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops

## feynman integrals

- » Analytic results for two-loop planar master integrals for Bhabha scattering
- » SAGEX Mathematica and Maple School Lectures
- » All Summer School Lectures for Amplitudes 2018
- » All Summer School Lectures for Amplitudes 2017

## field equations nonlinear

## field theories in higher dimensions

- » Unitarization from Geometry
- » A unitarity compatible approach to one-loop amplitudes with massive fermions

## field theories in lower dimensions

## field theory

- » Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
- » Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » Bipartite Graphs, On-Shell Diagrams, and Bipartite Field Theories: a Computational Package in Mathematica

## field theory conformal

- » All loop structures in Supergravity Amplitudes on $AdS_5 times S^5$ from CFT
- » Black holes in N=8 supergravity from SO(4,4) hidden symmetries
- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » Review of AdS/CFT Integrability: An Overview

## field theory massless

## field theory scalar

## field theory spinor

## finite field methods

## finite size effect

## five-loop

## five-point

## flow

## fluid

## flux tube

## form

## form factor

- » Three-loop color-kinematics duality: 24-dimensional solution space induced by new generalized gauge transformations
- » A Three-Point Form Factor Through Five Loops

## form factor sudakov

## form factor transition

- » The axial-vector contributions in two-photon reactions: pion transition form factor and deeply-virtual Compton scattering at NNLO in QCD
- » Dispersion relation for hadronic light-by-light scattering: pion pole

## form factor vertex

## formal aspects of field theory field theory in curved space

## formula

## four-point

- » Integrated One and Two Loop Four-Point Super-QCD
- » N=4 SYM and N=8 SG 5-loop integrands
- » Two-loop supersymmetric QCD and half-maximal supergravity integrands

## galileon

- » Covariant Color-Kinematics Duality
- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » One-loop renormalization in Galileon effective field theory

## gauge field theory

- » Extracting Einstein from the Loop-Level Double-Copy
- » Composing Effective Prediction at Five Points
- » Amplitudes from Coulomb to Kerr-Taub-NUT
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory
- » Soft gluon emission at two loops in full color
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Towards a Basis for Planar Two-Loop Integrals

## gauge field theory duality

## gauge field theory massive

## gauge field theory su(2)

## gauge field theory su(n)

## gauge field theory symmetry

## gauge field theory yang-mills

- » Covariant Color-Kinematics Duality
- » Four-loop collinear anomalous dimensions in QCD and $mathcal{N} = 4$ super Yang-Mills
- » Building Bases of Loop Integrands
- » Unitarization from Geometry
- » The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
- » Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
- » Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory
- » Two loop calculation of Yang-Mills propagators in the Curci-Ferrari model
- » Gravitational Radiation from Color-Kinematics Duality
- » Double-Copy Constructions and Unitarity Cuts
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
- » D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
- » Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
- » Bootstrapping the three-loop hexagon

## gauge field theory yang-mills supersymmetry

- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand

## gauge fixing

## gauge symmetry

- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
- » Building Bases of Loop Integrands
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
- » Color-Kinematics Duality for QCD Amplitudes
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops

## gauge theory

## gauge-gravity correspondence

## general relativity

- » Covariant Color-Kinematics Duality
- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
- » Scattering Amplitudes and Conservative Binary Dynamics at ${cal O}(G^4)$
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Scattering amplitudes in affine gravity
- » Mining the Geodesic Equation for Scattering Data
- » Unitarization from Geometry

## general relativity alternative theories of gravity

- » Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
- » Mining the Geodesic Equation for Scattering Data

## generalized parton distribution

## geodesic

## geometry

- » Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
- » Cluster patterns in Landau and Leading Singularities via the Amplituhedron
- » Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
- » Algebraic singularities of scattering amplitudes from tropical geometry
- » Positivity Sectors and the Amplituhedron

## ghost correlation function

## gluon

- » Soft gluon emission at two loops in full color
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » Inverse of the String Theory KLT Kernel
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Recursion in multiplet bases for tree-level MHV gluon amplitudes
- » Decomposing color structure into multiplet bases
- » All one-loop NMHV gluon amplitudes in N=1 SYM
- » Hexagon functions and the three-loop remainder function

## gluon correlation function

## gluon gluon elastic scattering

## gluon scattering amplitude

## gluon splitting

## gluons

- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Summer School Lectures for Amplitudes 2018
- » All Summer School Lectures for Amplitudes 2017

## goldstino

## graph methods

## graph theory

- » Bipartite Graphs, On-Shell Diagrams, and Bipartite Field Theories: a Computational Package in Mathematica
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

## grassmanian geometry

## grassmann

- » Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
- » How tropical are seven- and eight-particle amplitudes?
- » Algebraic singularities of scattering amplitudes from tropical geometry
- » Cluster adjacency properties of scattering amplitudes
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes

## gravitation

- » SAGEX 2021 PhD Organized Summer School
- » Composing Effective Prediction at Five Points
- » Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
- » Simple encoding of higher derivative gauge and gravity counterterms
- » Amplitudes from Coulomb to Kerr-Taub-NUT
- » The Two-Loop Four-Graviton Scattering Amplitudes
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory
- » Double copy for massive quantum particles with spin
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
- » Double-Copy Constructions and Unitarity Cuts
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory

## gravitation affine

## gravitation classical

- » Radiative Classical Gravitational Observables at $mathcal O(G^3)$ from Scattering Amplitudes
- » Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics

## gravitation dilaton

## gravitation duality

## gravitation einstein-hilbert

## gravitation emission

## gravitation fundamental constant

- » SUSY in the Sky with Gravitons
- » Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics

## gravitation interaction

- » Scattering amplitudes in affine gravity
- » Mining the Geodesic Equation for Scattering Data
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams

## gravitation massive

## gravitation model

## gravitation scattering amplitude

## gravitation weak field

- » Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies

## gravitational radiation

- » Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
- » Gravitational Radiation from Color-Kinematics Duality

## graviton

- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops

## graviton momentum

## graviton multiplet

## graviton scattering amplitude

## group galois

- » Cosmic Wheels: From integrability to the Galois coaction
- » The Cosmic Galois Group and Extended Steinmann Relations for Planar $mathcal{N} = 4$ SYM Amplitudes

## group representation

## group su(n) x su(n)

## hamiltonian

- » Scattering Amplitudes and Conservative Binary Dynamics at ${cal O}(G^4)$
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
- » Tidal Effects in the Post-Minkowskian Expansion
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory

## hbar expansion

## helicity

- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » Building Bases of Loop Integrands
- » How tropical are seven- and eight-particle amplitudes?
- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops

## helicity amplitude analysis

## helicity violation

- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand
- » Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

## hep-ph

## hep-th

- » Scattering amplitudes and form factors in EFT
- » Geometrical aspects of amplitudes and correlators in N=4 SYM
- » Classical Gravity from Gluon Interactions
- » On-shell techniques for Effective Field Theories
- » Massive 2- and 3-loop corrections to hard scattering processes in QCD
- » Perturbative integrability in 1+1 dimensions and affine Toda theories
- » Multipoint conformal blocks in conformal field theories
- » Closed. ~~A&I Group, Northwestern University~~
- » Non-planar anomalous dimensions in sYM theories
- » Coherent states and classical radiative observables in the S-matrix formalism
- » Unitarity approaches to two-loop all-plus amplitudes
- » Massive matter and the double copy -- Bootstrapping amplitudes in gauge and gravity theories
- » The On-Shell Highway To Waveforms
- » Heavy particles and the binary inspiral problem

## heterotic

## hidden symmetry

## higgs physics

## higher-dimensional

## higher-order

- » The axial-vector contributions in two-photon reactions: pion transition form factor and deeply-virtual Compton scattering at NNLO in QCD
- » The Double Pentaladder Integral to All Orders

## higher-order 0

## higher-order 1

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » The $ppto W(to lν)+γ$ process at next-to-next-to-leading order
- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » Tidal Effects in the Post-Minkowskian Expansion
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Gravitational Radiation from Color-Kinematics Duality

## higher-order 2

- » The $ppto W(to lν)+γ$ process at next-to-next-to-leading order
- » Master integrals for the NNLO virtual corrections to $q bar{q} rightarrow t bar{t}$ scattering in QCD: the non-planar graphs
- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand

## higher-order 4

- » Four-loop collinear anomalous dimensions in QCD and $mathcal{N} = 4$ super Yang-Mills
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops

## higher-order 5

## holography

## holomorphic

## infrared

- » Four-loop collinear anomalous dimensions in QCD and $mathcal{N} = 4$ super Yang-Mills
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » Two loop calculation of Yang-Mills propagators in the Curci-Ferrari model
- » Manifestly Dual-Conformal Loop Integration
- » Analytic result for a two-loop five-particle amplitude
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » Local integrands for two-loop all-plus Yang-Mills amplitudes

## infrared problem

## integrability

- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » Cosmic Wheels: From integrability to the Galois coaction
- » All Lectures for the first SAGEX scientific School (DESY)
- » The two-loop five-point amplitude in $mathcal{N} =4$ super-Yang-Mills theory
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Review of AdS/CFT Integrability: An Overview
- » Review of AdS/CFT Integrability: An Overview

## integral convergence

## integrand decomposition

## integrands

- » N=4 SYM and N=8 SG 5-loop integrands
- » Two-loop supersymmetric QCD and half-maximal supergravity integrands

## interaction gauge

## intercations with detector

## introductory

## invariance conformal

## invariance gauge

- » Simple encoding of higher derivative gauge and gravity counterterms
- » Tidal Effects in the Post-Minkowskian Expansion
- » Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory
- » Amplitudes at Infinity
- » Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity

## invariance yangian

## isoscalar

## iterated Eisenstein integrals

## iterated integrals

## jacobi identity

- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Gravitational Radiation from Color-Kinematics Duality

## jet methods

## kaluza-klein

## kerr

## kerr/cft correspondence

## kinematics

- » Covariant Color-Kinematics Duality
- » Massive Double Copy in Three Spacetime Dimensions
- » Composing Effective Prediction at Five Points
- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Simple encoding of higher derivative gauge and gravity counterterms
- » Soft gluon emission at two loops in full color
- » Double copy for massive quantum particles with spin
- » The Cosmic Galois Group and Extended Steinmann Relations for Planar $mathcal{N} = 4$ SYM Amplitudes
- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » Amplitudes at Infinity
- » Dispersion relation for hadronic light-by-light scattering: pion pole
- » Gravitational Radiation from Color-Kinematics Duality
- » The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Color-Kinematics Duality for QCD Amplitudes
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Double-Copy Constructions and Unitarity Cuts
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » Hexagon functions and the three-loop remainder function
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory

## kinematics multi-regge

- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

## landau gauge

## large ansatze

## lattice

## lattice anisotropy

## lattice field theories lattice qcd

## lattice field theory

## laurent expansion

- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity

## leading logarithm approximation

## lectures

- » SAGEX 2021 PhD Organized Summer School
- » SAGEX Mathematica and Maple School Lectures
- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Lectures for the first SAGEX scientific School (DESY)
- » All Summer School Lectures for Amplitudes 2018
- » All Summer School Lectures for Amplitudes 2017

## lepton mass

## letters

## localization

## loop amplitude

## loop integral

- » Analytic results for two-loop planar master integrals for Bhabha scattering
- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » All loop structures in Supergravity Amplitudes on $AdS_5 times S^5$ from CFT
- » All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » Planar two-loop integrals for $mathbf{μe}$ scattering in QED with finite lepton masses
- » A Three-Point Form Factor Through Five Loops
- » Radiative Classical Gravitational Observables at $mathcal O(G^3)$ from Scattering Amplitudes
- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » Cosmic Wheels: From integrability to the Galois coaction
- » Building Bases of Loop Integrands
- » Cluster patterns in Landau and Leading Singularities via the Amplituhedron
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » Soft gluon emission at two loops in full color
- » Two loop calculation of Yang-Mills propagators in the Curci-Ferrari model
- » Manifestly Dual-Conformal Loop Integration
- » The two-loop five-point amplitude in $mathcal{N} =4$ super-Yang-Mills theory
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals
- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » Dispersion relation for hadronic light-by-light scattering: pion pole
- » The Double Pentaladder Integral to All Orders
- » D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
- » Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
- » Towards a Basis for Planar Two-Loop Integrals

## loop integral 0

- » Ultraviolet Properties of N = 8 Supergravity at Five Loops

## loop integral 1

- » Extracting Einstein from the Loop-Level Double-Copy
- » One-loop matrix elements of effective superstring interactions: $α'$-expanding loop integrands
- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD

## loop integral 4

## mass effect

## mass formula

## mass ratio

- » Mining the Geodesic Equation for Scattering Data
- » Tidal Effects in the Post-Minkowskian Expansion

## mass spectrum

## mass topological

## massive spinor helicity

## master integral

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Analytic results for two-loop planar master integrals for Bhabha scattering
- » Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory
- » Master integrals for the NNLO virtual corrections to $q bar{q} rightarrow t bar{t}$ scattering in QCD: the non-planar graphs
- » Analytic result for a two-loop five-particle amplitude
- » The two-loop five-point amplitude in $mathcal{N} =4$ super-Yang-Mills theory
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs
- » All one-loop NMHV gluon amplitudes in N=1 SYM
- » Towards a Basis for Planar Two-Loop Integrals

## mathematica

- » Converting from Schnetz f-alphabet to MZVs through weight 14
- » Integrated One and Two Loop Four-Point Super-QCD
- » Six-Gluon Amplitudes in Planar N=4 Super-Yang-Mills Theory at Six and Seven Loops
- » The two-loop five-point amplitude in N=8 supergravity
- » A Monte Carlo Approach to the 4D Scattering Equations
- » N=4 SYM and N=8 SG 5-loop integrands
- » Amplitudes related Graph Tools
- » Bourjaily -- Mathematica for N=4 Tree Amplitudes

## mathematical methods

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Extracting Einstein from the Loop-Level Double-Copy
- » Planar two-loop integrals for $mathbf{μe}$ scattering in QED with finite lepton masses
- » Radiative Classical Gravitational Observables at $mathcal O(G^3)$ from Scattering Amplitudes
- » How tropical are seven- and eight-particle amplitudes?
- » Algebraic singularities of scattering amplitudes from tropical geometry
- » Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » Manifestly Dual-Conformal Loop Integration
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop

## maximally helicity violating amplitude

- » Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
- » All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » How tropical are seven- and eight-particle amplitudes?
- » Cluster patterns in Landau and Leading Singularities via the Amplituhedron
- » The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
- » Algebraic singularities of scattering amplitudes from tropical geometry
- » Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
- » Amplitudes at Infinity
- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Cluster adjacency properties of scattering amplitudes
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
- » Recursion in multiplet bases for tree-level MHV gluon amplitudes
- » Hexagon functions and the three-loop remainder function
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand

## mellin transformation

- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » The Double Pentaladder Integral to All Orders

## meson mass spectrum

## method of maximal cuts

## modified gravity

## moduli

## moduli space

- » Bipartite Graphs, On-Shell Diagrams, and Bipartite Field Theories: a Computational Package in Mathematica
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

## momentum dependence

## momentum twistors

## monodromy

## monte-carlo

## multi-regge

- » Analytic result for a two-loop five-particle amplitude
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Bootstrapping an NMHV amplitude through three loops
- » Hexagon functions and the three-loop remainder function
- » Bootstrapping the three-loop hexagon

## multi-regge kinematics

## multiple polylogarithms

## multiple zeta values

## multiplet

- » Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
- » Recursion in multiplet bases for tree-level MHV gluon amplitudes
- » Decomposing color structure into multiplet bases
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
- » Orthogonal multiplet bases in SU(Nc) color space

## multiplet coupling

## multiplet vector

- » Black holes in N=8 supergravity from SO(4,4) hidden symmetries
- » N=4 conformal supergravity: the complete actions

## multiplicity

- » All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » Building Bases of Loop Integrands
- » Amplitudes at Infinity
- » Berends-Giele recursion for double-color-ordered amplitudes

## multiplicity high

## muon magnetic moment

## muon mass

- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## n-point function

- » One-loop renormalization in Galileon effective field theory
- » Cluster adjacency properties of scattering amplitudes

## n-point function 3

- » Extracting Einstein from the Loop-Level Double-Copy
- » Amplitudes from Coulomb to Kerr-Taub-NUT
- » Two loop calculation of Yang-Mills propagators in the Curci-Ferrari model

## n-point function 4

- » Extracting Einstein from the Loop-Level Double-Copy
- » All loop structures in Supergravity Amplitudes on $AdS_5 times S^5$ from CFT
- » Composing Effective Prediction at Five Points
- » A Three-Point Form Factor Through Five Loops
- » The Origin of the Six-Gluon Amplitude in Planar $mathcal{N}=4$ SYM
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- » Color-Kinematics Duality in One-Loop Four-Gluon Amplitudes with Matter
- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

## n-point function 5

- » Extracting Einstein from the Loop-Level Double-Copy
- » Massive Double Copy in Three Spacetime Dimensions
- » Composing Effective Prediction at Five Points
- » The two-loop five-point amplitude in $mathcal{N} =4$ super-Yang-Mills theory
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals

## n-point function 6

- » Extracting Einstein from the Loop-Level Double-Copy
- » The Double Pentaladder Integral to All Orders
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand
- » Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

## n-point function 8

## n=8 supergravity

## neutron star

## nlo computations

- » The $ppto W(to lν)+γ$ process at next-to-next-to-leading order
- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## nonlocal

## nonperturbative effects

- » Dispersion relation for hadronic light-by-light scattering: pion pole
- » The Double Pentaladder Integral to All Orders

## numerical calculations

- » The $ppto W(to lν)+γ$ process at next-to-next-to-leading order
- » A Three-Point Form Factor Through Five Loops
- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand

## numerical methods

## numerical methods variational

## on-shell

- » Local integrands for two-loop all-plus Yang-Mills amplitudes
- » Positivity Sectors and the Amplituhedron

## one-loop

## onshell diagrams

## onshell methods

## operator bps

## operator higher-dimensional

- » Simple encoding of higher derivative gauge and gravity counterterms
- » Structure of two-loop SMEFT anomalous dimensions via on-shell methods

## operator product expansion

- » A Three-Point Form Factor Through Five Loops
- » The Origin of the Six-Gluon Amplitude in Planar $mathcal{N}=4$ SYM
- » Bootstrapping an NMHV amplitude through three loops
- » Hexagon functions and the three-loop remainder function
- » Bootstrapping the three-loop hexagon

## optical theorem

## orbit

- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics

## overlap

- » The two-loop five-point amplitude in $mathcal N=8$ supergravity

## p p scattering

## p p to w photon

## parametrization

## parity

## particle massive

- » Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
- » Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » Double copy for massive quantum particles with spin

## particle spin

## parton distribution function

## parton distribution functions

## parton scattering

## parton scattering amplitude

## parton shower

## path permutations

## periods

## perturbation

## perturbation theory

- » Two loop calculation of Yang-Mills propagators in the Curci-Ferrari model
- » On the Renormalization of the Effective Field Theory of Large Scale Structures

## perturbation theory higher-order

## perturbative qcd

- » Soft gluon emission at two loops in full color
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals
- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » Local integrands for two-loop all-plus Yang-Mills amplitudes

## phase space

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Planar two-loop integrals for $mathbf{μe}$ scattering in QED with finite lepton masses
- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)

## photon photon scattering

## physcis of the early universe

## pi pole

## planar

- » Converting from Schnetz f-alphabet to MZVs through weight 14
- » Six-Gluon Amplitudes in Planar N=4 Super-Yang-Mills Theory at Six and Seven Loops

## poincare

## polarization vector

## pole

- » Massive Double Copy in Three Spacetime Dimensions
- » Four-loop collinear anomalous dimensions in QCD and $mathcal{N} = 4$ super Yang-Mills

## pole massless

## polyakov loop

## positive geometries

## positivity

## postdoc

## power spectrum

- » On the Renormalization of the Effective Field Theory of Large Scale Structures
- » On the Renormalization of the Effective Field Theory of Large Scale Structures

## precision qed

- » Analytic results for two-loop planar master integrals for Bhabha scattering
- » Dispersion relation for hadronic light-by-light scattering: pion pole

## predictions

## pressure

## propagator

## propagator feynman

- » One-loop matrix elements of effective superstring interactions: $α'$-expanding loop integrands
- » Inverse of the String Theory KLT Kernel

## qcd

- » Color-Kinematics Duality for QCD Amplitudes
- » Recursion in multiplet bases for tree-level MHV gluon amplitudes
- » All one-loop NMHV gluon amplitudes in N=1 SYM

## qcd phenomenology

- » The $ppto W(to lν)+γ$ process at next-to-next-to-leading order
- » Decomposing color structure into multiplet bases

## quantum chromodynamics

- » The $ppto W(to lν)+γ$ process at next-to-next-to-leading order
- » Three-loop color-kinematics duality: 24-dimensional solution space induced by new generalized gauge transformations
- » A Three-Point Form Factor Through Five Loops
- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » Local integrands for two-loop all-plus Yang-Mills amplitudes
- » Color-Kinematics Duality for QCD Amplitudes
- » Decomposing color structure into multiplet bases

## quantum chromodynamics massless

## quantum chromodynamics perturbation theory

- » Orthogonal multiplet bases in SU(Nc) color space

## quantum chromodynamics scattering amplitude

## quantum chromodynamics supersymmetry

- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

## quantum electrodynamics

- » Analytic results for two-loop planar master integrals for Bhabha scattering
- » Planar two-loop integrals for $mathbf{μe}$ scattering in QED with finite lepton masses

## quantum electrodynamics correction

- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## quantum field theory in curved spacetime

## quantum gravity

- » Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
- » Scattering amplitudes in affine gravity

## quark antiquark pair

- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
- » Decomposing color structure into multiplet bases

## quark antiquark scattering

## quark antiquark to top anti-top

## quark flavor 3

## quark gluon

## quark mass dependence

## quark massive

## quark wilson

## radiation classical

## radiation effect

## radiation emission

## radiative correction

## regularization

- » Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
- » Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory
- » Manifestly Dual-Conformal Loop Integration

## regularization dimensional

- » Analytic result for a two-loop five-particle amplitude
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals

## renormalization

- » Structure of two-loop SMEFT anomalous dimensions via on-shell methods
- » One-loop renormalization in Galileon effective field theory
- » One-loop renormalization in Galileon effective field theory
- » On the Renormalization of the Effective Field Theory of Large Scale Structures

## renormalization group

## representation

## resonance mass spectrum

## resummation

- » The Origin of the Six-Gluon Amplitude in Planar $mathcal{N}=4$ SYM
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » One-loop renormalization in Galileon effective field theory

## riemann

- » The Two-Loop Four-Graviton Scattering Amplitudes
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

## rotation

## s-matrix

- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD
- » Gravitational Radiation from Color-Kinematics Duality
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string

## scalar particle scattering amplitude

## scale dependence

## scaling

## scattering

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Tidal Effects in the Post-Minkowskian Expansion
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » The Two-Loop Four-Graviton Scattering Amplitudes
- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » Hexagon functions and the three-loop remainder function

## scattering amplitude

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
- » Extracting Einstein from the Loop-Level Double-Copy
- » Covariant Color-Kinematics Duality
- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Massive Double Copy in Three Spacetime Dimensions
- » All loop structures in Supergravity Amplitudes on $AdS_5 times S^5$ from CFT
- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » Scattering Amplitudes and Conservative Binary Dynamics at ${cal O}(G^4)$
- » Composing Effective Prediction at Five Points
- » Radiative Classical Gravitational Observables at $mathcal O(G^3)$ from Scattering Amplitudes
- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » Simple encoding of higher derivative gauge and gravity counterterms
- » Amplitudes from Coulomb to Kerr-Taub-NUT
- » Mining the Geodesic Equation for Scattering Data
- » Building Bases of Loop Integrands
- » How tropical are seven- and eight-particle amplitudes?
- » Tidal Effects in the Post-Minkowskian Expansion
- » Cluster patterns in Landau and Leading Singularities via the Amplituhedron
- » Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
- » The Origin of the Six-Gluon Amplitude in Planar $mathcal{N}=4$ SYM
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » The Two-Loop Four-Graviton Scattering Amplitudes
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory
- » Soft gluon emission at two loops in full color
- » Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » Double copy for massive quantum particles with spin
- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD
- » Analytic result for a two-loop five-particle amplitude
- » The two-loop five-point amplitude in $mathcal{N} =4$ super-Yang-Mills theory
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
- » Cluster adjacency properties of scattering amplitudes
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
- » Color-Kinematics Duality for QCD Amplitudes
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
- » Bootstrapping an NMHV amplitude through three loops
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
- » Towards a Basis for Planar Two-Loop Integrals

## scattering amplitude pole

## scattering amplitude singularity

- » Algebraic singularities of scattering amplitudes from tropical geometry
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand

## scattering amplitude unitarity

## scattering amplitude yang-mills

## scattering amplitudes

- » Analytic results for two-loop planar master integrals for Bhabha scattering
- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Massive Double Copy in Three Spacetime Dimensions
- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » Composing Effective Prediction at Five Points
- » A Three-Point Form Factor Through Five Loops
- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
- » Building Bases of Loop Integrands
- » Unitarization from Geometry
- » How tropical are seven- and eight-particle amplitudes?
- » Structure of two-loop SMEFT anomalous dimensions via on-shell methods
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams
- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory
- » Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted Projective Space
- » Soft gluon emission at two loops in full color
- » Algebraic singularities of scattering amplitudes from tropical geometry
- » Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » Double copy for massive quantum particles with spin
- » The Cosmic Galois Group and Extended Steinmann Relations for Planar $mathcal{N} = 4$ SYM Amplitudes
- » All Lectures for the first SAGEX scientific School (DESY)
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals
- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Gravitational Radiation from Color-Kinematics Duality
- » The Double Pentaladder Integral to All Orders
- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
- » Inverse of the String Theory KLT Kernel
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Local integrands for two-loop all-plus Yang-Mills amplitudes
- » Color-Kinematics Duality for QCD Amplitudes
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
- » Recursion in multiplet bases for tree-level MHV gluon amplitudes
- » Bootstrapping an NMHV amplitude through three loops
- » Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
- » All one-loop NMHV gluon amplitudes in N=1 SYM
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory

## scattering classical

## scattering equations

## scattering gravitation

- » SUSY in the Sky with Gravitons
- » Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics

## scattering-equations

## self-duality

## seven-loop

## sigma model nonlinear

- » Covariant Color-Kinematics Duality
- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string

## sigma models

## simplex

- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

## singularity

- » Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » An Elliptic Yangian-Invariant, `Leading Singularity'
- » Cluster patterns in Landau and Leading Singularities via the Amplituhedron
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » Dispersion relation for hadronic light-by-light scattering: pion pole
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Local integrands for two-loop all-plus Yang-Mills amplitudes
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

## singularity ultraviolet

## six-loop

## six-point

## sl(2 r)

## sl(n)

## so(4 4)

## software

- » Converting from Schnetz f-alphabet to MZVs through weight 14
- » A Monte Carlo Approach to the 4D Scattering Equations
- » Amplitudes related Graph Tools
- » Non-abelian Z-theory
- » Bourjaily -- Mathematica for N=4 Tree Amplitudes

## space calabi-yau

## space-time

## space-time dimension 3

## space-time dimension 4

- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## space-time schwarzschild

## spectral

## spectrum discrete

## sphere

## spin

- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Double copy for massive quantum particles with spin

## spin 2

## spin chains

## spin effect

## spinless

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory

## spinning massive particles

## spinor

## spinor helicity

## splitting functions

## star

## star binary

## star massive

## string

- » Inverse of the String Theory KLT Kernel
- » Berends-Giele recursion for double-color-ordered amplitudes

## string amplitudes

- » All Lectures for the first SAGEX scientific School (DESY)
- » All Summer School Lectures for Amplitudes 2018

## string correlation function

## string massless

## string model

- » The Origin of the Six-Gluon Amplitude in Planar $mathcal{N}=4$ SYM
- » Inverse of the String Theory KLT Kernel

## string model boson

## string model compactification

## string model effective action

## string open

## string tension

## string theory

## string theory quantum gravity gauge/gravity duality

## string-theory

## strong coupling

## strong interactions

## structure

- » Structure of two-loop SMEFT anomalous dimensions via on-shell methods
- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD
- » Recursion in multiplet bases for tree-level MHV gluon amplitudes
- » Decomposing color structure into multiplet bases
- » On the Renormalization of the Effective Field Theory of Large Scale Structures

## stu model

## su(1 1)/u(1)

## su(3)

## su(n)

- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » Decomposing color structure into multiplet bases
- » Orthogonal multiplet bases in SU(Nc) color space

## sum rule

## super yang-mills

## superfield

## supergravity

- » One-loop matrix elements of effective superstring interactions: $α'$-expanding loop integrands
- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Ultraviolet Properties of N = 8 Supergravity at Five Loops
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops

## supergravity 2

## supergravity 4

## supergravity 5

## supergravity 6

## supergravity 8

- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
- » Radiative Classical Gravitational Observables at $mathcal O(G^3)$ from Scattering Amplitudes
- » Black holes in N=8 supergravity from SO(4,4) hidden symmetries
- » Amplitudes at Infinity
- » The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory

## supergravity action

## supergravity conformal

## supergravity duality

## supergravity models

- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » N=4 conformal supergravity: the complete actions
- » The two-loop five-particle amplitude in $mathcal{N}=8$ supergravity
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

## superspaces

## superstring open

## superstrings and heterotic strings

- » Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
- » Inverse of the String Theory KLT Kernel
- » Berends-Giele recursion for double-color-ordered amplitudes

## supersymmetric gauge theory

- » A Three-Point Form Factor Through Five Loops
- » How tropical are seven- and eight-particle amplitudes?
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
- » Four-graviton scattering to three loops in ${mathcal N}=8$ supergravity
- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
- » All one-loop NMHV gluon amplitudes in N=1 SYM
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops

## supersymmetry

- » Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
- » Simple encoding of higher derivative gauge and gravity counterterms
- » The Origin of the Six-Gluon Amplitude in Planar $mathcal{N}=4$ SYM
- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Lectures for the first SAGEX scientific School (DESY)
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
- » Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
- » Color-Kinematics Duality for QCD Amplitudes
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

## supersymmetry 1

## supersymmetry 2

- » SUSY in the Sky with Gravitons
- » Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
- » The Full-Color Two-Loop Four-Gluon Amplitude in $mathcal{N} = 2$ Super-QCD
- » Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
- » Hidden Supersymmetry May Imply Duality Invariance

## supersymmetry 4

- » Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
- » All loop structures in Supergravity Amplitudes on $AdS_5 times S^5$ from CFT
- » All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
- » A Three-Point Form Factor Through Five Loops
- » All-order amplitudes at any multiplicity in the multi-Regge limit
- » How tropical are seven- and eight-particle amplitudes?
- » Cluster patterns in Landau and Leading Singularities via the Amplituhedron
- » The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
- » Soft gluon emission at two loops in full color
- » Algebraic singularities of scattering amplitudes from tropical geometry
- » Manifestly Dual-Conformal Loop Integration
- » Analytic result for a two-loop five-particle amplitude
- » The two-loop five-point amplitude in $mathcal{N} =4$ super-Yang-Mills theory
- » Amplitudes at Infinity
- » The Multi-Regge Limit of the Eight-Particle Amplitude Beyond Leading Logarithmic Accuracy
- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » The Double Pentaladder Integral to All Orders
- » The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- » Cluster adjacency properties of scattering amplitudes
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
- » Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes
- » Bootstrapping an NMHV amplitude through three loops
- » Hexagon functions and the three-loop remainder function
- » Local integrands for the five-point amplitude in planar N=4 SYM up to five loops
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
- » Global Poles of the Two-Loop Six-Point N=4 SYM integrand
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops
- » Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
- » Bootstrapping the three-loop hexagon

## supersymmetry hidden symmetry

- » Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
- » Hidden Supersymmetry May Imply Duality Invariance

## symmetry conformal

- » The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
- » A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

## symmetry crossing

## symmetry discrete

## symmetry gauge

## taub-nut

## taylor expansion

- » Master integrals for the NNLO virtual corrections to $μe$ scattering in QED: the non-planar graphs

## tension

## tensor energy-momentum

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » A Three-Point Form Factor Through Five Loops

## tensor killing

## tensor weyl

## top mass

## top pair production

## topological

## topological expansion for strings

## topological field theories

## topology

## torus

## tracking

## transcendental weight

## transformation gauge

## tree approximation

- » The $ppto W(to lν)+γ$ process at next-to-next-to-leading order
- » The Eikonal Approach to Gravitational Scattering and Radiation at $mathcal O(G^3)$
- » All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
- » Composing Effective Prediction at Five Points
- » Kinematic numerators from the worldsheet: cubic trees from labelled trees
- » Scattering amplitudes in affine gravity
- » Simple encoding of higher derivative gauge and gravity counterterms
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » Double copy for massive quantum particles with spin
- » Analytic result for a two-loop five-particle amplitude
- » Abelian Z-theory: NLSM amplitudes and alpha'-corrections from the open string
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » Local integrands for two-loop all-plus Yang-Mills amplitudes
- » Berends-Giele recursion for double-color-ordered amplitudes
- » Color-Kinematics Duality for QCD Amplitudes
- » Recursion in multiplet bases for tree-level MHV gluon amplitudes
- » Color-Kinematic Duality in ABJM Theory Without Amplitude Relations
- » Towards a Basis for Planar Two-Loop Integrals

## tree level

## tree-level

## trees and forests

## triality

## triangulation

## two-loop

- » Integrated One and Two Loop Four-Point Super-QCD
- » The two-loop five-point amplitude in N=8 supergravity
- » Two-loop supersymmetric QCD and half-maximal supergravity integrands

## two-photon

## u-duality

## ultraviolet

- » Building Bases of Loop Integrands
- » The Two-Loop Four-Graviton Scattering Amplitudes
- » Ultraviolet Properties of N = 8 Supergravity at Five Loops
- » The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
- » Double-Copy Constructions and Unitarity Cuts
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
- » The Ultraviolet Behavior of N=8 Supergravity at Four Loops

## uniform lightcone gauge

## unitarity

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » Scattering Amplitudes and Conservative Binary Dynamics at ${cal O}(G^4)$
- » Radiative Classical Gravitational Observables at $mathcal O(G^3)$ from Scattering Amplitudes
- » Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
- » The Two-Loop Four-Graviton Scattering Amplitudes
- » Black Hole Binary Dynamics from the Double Copy and Effective Theory
- » Analytic Form of the Three-loop Four-gluon Scattering Amplitudes in Yang-Mills Theory
- » The $b_1$ resonance in coupled $πω$, $πφ$ scattering from lattice QCD
- » Differential equations from unitarity cuts: nonplanar hexa-box integrals
- » The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- » A unitarity compatible approach to one-loop amplitudes with massive fermions
- » Local integrands for two-loop all-plus Yang-Mills amplitudes
- » Double-Copy Constructions and Unitarity Cuts

## velocity

- » Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity
- » Quadratic-in-Spin Hamiltonian at $mathcal{O}(G^2)$ from Scattering Amplitudes
- » Classical Gravitational Scattering at ${cal O}(G^3)$ from Feynman Diagrams

## velocity dependence

## vertex operators

## video

- » SAGEX 2021 PhD Organized Summer School
- » SAGEX Mathematica and Maple School Lectures
- » All Lectures for the second SAGEX scientific School (Homboldt-University-Berlin)
- » All Lectures for the first SAGEX scientific School (DESY)
- » All Summer School Lectures for Amplitudes 2018
- » Amplitudes related Graph Tools
- » All Summer School Lectures for Amplitudes 2017

## virtual corrections

## wave model

## weak coupling

## wilson loop

- » Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
- » All orders results for self-crossing Wilson loops mimicking double parton scattering
- » Bootstrapping an NMHV amplitude through three loops
- » Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
- » Bootstrapping the three-loop hexagon

## wilson ’t hooft and polyakov loops

## yang-mills

- » Efficient Calculation of Crossing Symmetric BCJ Tree Numerators
- » Simple encoding of higher derivative gauge and gravity counterterms
- » String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
- » The two-loop five-point amplitude in $mathcal N=8$ supergravity
- » Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops
- » The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory

## yang-mills supersymmetry

- » Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
- » Four-loop collinear anomalous dimensions in QCD and $mathcal{N} = 4$ super Yang-Mills
- » An Elliptic Yangian-Invariant, `Leading Singularity'
- » Building Bases of Loop Integrands
- » Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
- » Hexagon functions and the three-loop remainder function
- » The Differential of All Two-Loop MHV Amplitudes in N=4 Yang-Mills Theory
- » D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops