Jekyll2023-03-30T05:47:14+00:00https://amplitudes.org/feed.xmlAmplitudes.orgComing soon.John Joseph M. CarrascoScattering amplitudes and form factors in EFT2022-11-29T00:00:00+00:002022-11-29T00:00:00+00:00https://amplitudes.org/theses/DeAngelis<h1 id="scattering-amplitudes-and-form-factors-in-eft">Scattering amplitudes and form factors in EFT</h1>
<h3 id="stefano-de-angelis">Stefano De Angelis</h3>
<h2 id="link-to-pdf"><a href="/images/StefanoDeAngelisThesis.pdf">Link to PDF</a></h2>
<h2 id="abstract">Abstract</h2>
<p>The central theme of the thesis is the application of modern on-shell techniques to compute Scattering Amplitudes and Form Factors in various Effective Field Theories. In particular, we apply such techniques in the context of the Standard Model Effective Field Theories, focusing on the renormalisation group evolution of irrelevant operators, and the study of the classical binary problem in gravitational theories, beyond General Relativity including higher derivative interactions.</p>
<p>We first show how to find a basis of EFT interactions from a purely on-shell point of view. From these EFT building blocks, any tree-level amplitude can be computed using a recursive algorithm which requires only the knowledge of lower-point amplitudes. Starting from these results, modern (generalised) unitarity techniques allow for the computations of higher loop amplitudes which can be used to characterise precision observables both for gravitational waves and for collider experiments. We will focus on the computation of form factors in the context of Standard Model Effective Field Theory which allowed us to compute for the first time the one-loop mixing matrix for all the dimension-eight operators in the theory. Then, we will show how to compute the deflection angle and the time delays induced by higher-derivative corrections to the Einstein-Hilbert action from the eikonal form of gravitational scattering amplitudes.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoStefano De Angelis's thesisGeometrical aspects of amplitudes and correlators in N=4 SYM2022-10-01T00:00:00+00:002022-10-01T00:00:00+00:00https://amplitudes.org/theses/Dian<h1 id="geometrical-aspects-of-amplitudes-and-correlators-in-n4-sym">Geometrical aspects of amplitudes and correlators in N=4 SYM</h1>
<h3 id="gabriele-dian">Gabriele Dian</h3>
<h2 id="link-to-pdf"><a href="/images/Gabriele%20Dian%20thesis.pdf">Link to PDF</a></h2>
<h2 id="abstract">Abstract</h2>
<p>This thesis describes progresses made by the author and collaborators in the positive geometry description of superamplitudes and the supercorrelators in planar N = 4 SYM.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoGabriele Dian's thesisClassical Gravity from Gluon Interactions2022-08-26T00:00:00+00:002022-08-26T00:00:00+00:00https://amplitudes.org/theses/CShi<h1 id="classical-gravity-from-gluon-interactions">Classical Gravity from Gluon Interactions</h1>
<h3 id="canxin-shi">Canxin Shi</h3>
<h2 id="link-to-pdf"><a href="/images/Dissertation_Shi_Canxin_2022-11-29.pdf">Link to PDF</a></h2>
<h2 id="abstract">Abstract</h2>
<p>This thesis focuses on the double copy relation between gauge theories and gravity and its application in the classical scattering of massive compact objects. The double copy relation states that observables in a gravitational theory can be derived from “squaring” corresponding quantities in a gauge theory. It allows using modern techniques of gauge theories to tackle problems such as black hole scattering in gravity.
We first consider massive scalar quantum chromodynamics (SQCD) and perform the double copy procedure for the scattering amplitudes. We reconstruct the effective Lagrangian from the resulting amplitudes. It yields a gravitational theory of massive scalars coupled to gravity, axion, and dilaton. Additionally, it also produces scalar self-interaction terms. The emerging Lagrangian is constructed explicitly up to the sixth order of scalar fields, and an all-order form is conjectured.</p>
<p>It is followed by exploring the double copy of massive point particles, which can be seen as the classical version of the SQCD double copy. The source objects are formulated by worldline quantum field theories coupled to Yang-Mills, bi-adjoint scalar, and two-form-dilaton-gravity. We propose a double copy prescription for the eikonal phases, which can be used to derive observables such as momentum deflection and check it explicitly up to next-to-leading order
(NLO). We demonstrate its relation to the classical limit of scattering amplitudes and explain its extension to classical radiation.</p>
<p>We also investigate the non-perturbative double copy of classical solutions. Specifically, we extend the Kerr-Schild mapping, which allows obtaining solutions of the Einstein equation from that of gauge theory, to the case of a probe particle moving in the Kerr-Schild background. The orbits of a test charge in non-Abelian Coulomb background and on the equatorial plane of the spinning Kerr-like background are analyzed and categorized. We also find a new double copy between the conserved charges on the gauge theory and the gravity sides, which works naturally for both bound and unbound states.</p>
<p>Additionally, we study the Post-Minkowskian (PM) and Post-Newtonian (PN) expansions of the gravitational three-body effective potential. We provide a formal non-local result at 2PM and expand it in the slow-motion limit. We recover the interaction terms up to $G^2v^2$ and present the novel $G^2v^4$-contributions at 3PN. To obtain 2PM contributions to higher order in PN, we compute a family of 3-point integrals from a Yangian bootstrap approach.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoCanxin Shi's thesisOn-shell techniques for Effective Field Theories2022-07-25T00:00:00+00:002022-07-25T00:00:00+00:00https://amplitudes.org/theses/Huber<h1 id="on-shell-techniques-for-effective-field-theories">“On-shell techniques for Effective Field Theories”</h1>
<h3 id="manual-a-hubers-thesis">Manual A. Huber’s thesis</h3>
<h2 id="link-to-pdf"><a href="/images/Manuel_Huber_Thesis.pdf">Link to PDF</a></h2>
<h2 id="abstract">Abstract</h2>
<p>In this thesis I explore a wide range of applications of the so called on-shell methods to Effective Field Theories of gravity and the Standard Model. I will first focus on the tree- level and restrict my attention to four space-time dimensions where the use of spinor- helicity formalism allows for very compact expressions of gauge-invariant quantities as well as the simple classification of contact interactions from the assumptions of locality, Lorentz-invariance and little-group covariance. I discuss how to use unitarity to combine these contact terms into higher-multiplicity tree amplitudes and non-minimal form factors, providing an algorithm which makes only use of on-shell seeds but at the same time is applicable to any given EFT of massless particles. The tree-level results obtained in this first section provide then the necessary input for the results obtained in the remainder of the thesis, where unitarity and generalised unitarity is used to obtain loop-results from trees. In particular, I first discuss the computation of the one-loop mixing matrix of the full set of mass-dimension eight operators in a Standard Model EFT setting and then move on to applications in the context of gravity. Here, amplitudes techniques are used to extract classical information hiding in the perturbative expansion of gravitational theories beyond leading order. More specifically I will consider higher-derivative interactions involving powers of the Riemann tensor and study their effect on observables such as the bending angle and the time delay in a light particle deflection process. I also consider the interactions of heavy binaries mediated by such operators and study their impact on the power radiated through gravitational waves. Finally I discuss how to use six-dimensional spinor-helicity to bypass intrinsic limitations of the four-dimensional unitarity calculations, generalising known techniques for amplitudes to the case of form factors.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoManual A. Huber's thesisMassive 2- and 3-loop corrections to hard scattering processes in QCD2022-07-14T00:00:00+00:002022-07-14T00:00:00+00:00https://amplitudes.org/theses/Saragnese<h1 id="massive-2--and-3-loop-corrections-to-hard-scattering-processes-in-qcd">Massive 2- and 3-loop corrections to hard scattering processes in QCD</h1>
<h3 id="marco-saragnese">Marco Saragnese</h3>
<h2 id="link-to-pdf"><a href="/images/Marco%20Saragnese%20thesis.pdf">Link to PDF</a></h2>
<h2 id="abstract">Abstract</h2>
<p>This thesis deals with calculations of higher-order corrections in perturbative quantum chromodynamics (QCD). The two-mass contributions to the 3-loop, polarized twist-two operator matrix elements (OMEs) Qq and ggQ are calculated. The N-space result for ggQ is obtained analytically as a function of the quark mass ratio, which for Qq is not yet possible. In the z-space representation, one obtains for both matrix elements semi-analytical representations in terms of iterated integrals, whereby for reasons of efficiency an additional integral is necessary for some terms.</p>
<p>These universal (process-independent) massive OMEs govern the asymptotic behaviour of the Wilson coefficients in deep-inelastic scattering at large virtualities Q2 ≫ m2c,b, with mc,b the charm and bottom quark masses. These corrections are also required to define the variable flavour number scheme. This scheme describes the transition from massive quark corrections to the massless ones for very high momentum scales, which is relevant to the description of collider data.</p>
<p>In the single-mass, polarized case, we derive the logarithmic corrections for the Wilson coef- ficients of the structure function g1 in the asymptotic region Q2 ≫ m2c,b. This is done using the known OMEs and massless Wilson coefficients, using the renormalization group equations.</p>
<p>For the non-singlet structure functions $F_2^{NS}$ and $g_1^{NS}$ we revisit the scheme-invariant evolution
operator known for massless quarks and extend it to the massive case with single- and two-mass corrections. In this case, the evolution can effectively be described up to O($a^3_s$) in the Wilson coefficients, where as = αs/(4π) denotes the strong coupling constant. The influence of the hitherto not fully known 4-loop non-singlet anomalous dimension can be described effectively. It turns out that the effect of the theory error in question can be completely controlled. A representation by a Pad ́e approximant proves to be sufficient.</p>
<p>We consider the class of functions of multivariate hypergeometric series and study systems of differential equations obeyed by them. We describe an algorithmic method to solve some classes of such differential systems which delivers a hypergeometric series solution having nested hypergeometric products as summand; we discuss the relationship between these products and Pochhammer symbols. For a number of classical hypergeometric series we derive differential systems and their associated difference equations. We present some examples of series expan- sions of such functions and of the mathematical objects which arise therein. We also present a Mathematica package which implements algorithms related to the solution of partial linear dif- ference equations, focusing in particular on bounding the degree of the denominator of solutions which are rational functions. These methods are of particular importance when solving multi-leg calculations for Feynman diagrams, but also come into play when hypergeometric methods for multi-loop integrals are used.</p>
<p>We describe a numerical implementation of an N-space library for the calculation of scal-
ing violations for structure functions, which can perform the evolution of parton distribution
functions up to NNLO from a parametrization chosen by the user, and encodes massless and
massive Wilson coefficients for the structure functions $F_2$ and $g_1$ in the case of photon exchange,
and for the structure functions in the case of charged-current exchange. The library
contains analytic continuation of the relevant harmonic sums in Mellin-space up to weight 5 and many weight-6 harmonic sums.
The numerical representation in x space is performed by contour integration around the singularities of the solution of the evolution equations in N space.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoMarco Saragnese's thesisPerturbative integrability in 1+1 dimensions and affine Toda theories2022-05-01T00:00:00+00:002022-05-01T00:00:00+00:00https://amplitudes.org/theses/Polvara<h1 id="perturbative-integrability-in-11-dimensions-and-affine-toda-theories">Perturbative integrability in 1+1 dimensions and affine Toda theories</h1>
<h3 id="davide-polvara">Davide Polvara</h3>
<h2 id="link-to-pdf"><a href="/images/Davide%20Polvara%20thesis.pdf">Link to PDF</a></h2>
<h2 id="abstract">Abstract</h2>
<p>In this thesis, the perturbative integrability of 1+1 dimensional bosonic massive quantum field theories is investigated. Starting from a theory with a generic polynomial-like potential, the constraints on the masses and Lagrangian couplings emerging by requiring purely elastic amplitudes at the tree level are obtained. It is observed that theories satisfying these constraints are completely determined by their mass ratios and 3-point couplings, while all the higher-order couplings can be obtained recursively in terms of them by imposing the absence of production for higher numbers of external legs. By exploiting different root system properties, it is shown that all the bosonic affine Toda field theories universally satisfy the constraints of purely elasticity at the tree level: a complete proof of their tree-level integrability is therefore provided. Subsequently, the higher-order poles observed in the bootstrapped S-matrices of the ADE series of affine Toda models are studied in perturbation theory. These singular points have been explained in the past in terms of anomalous threshold singularities in certain Feynman diagrams, where multiple propagators go on-shell simultaneously in loop integrations. Networks of Feynman diagrams contributing to these higher-order poles are found and residues at the poles are obtained through perturbation theory, showing agreement with the bootstrapped results. We show that the residues are generated by suitably cutting the loop diagrams into products of tree-level graphs, which will be called ‘atoms’. Most of these atoms simplify between one another and only a small number of them survive matching the bootstrapped results. The simplification mechanism between atoms inside networks is reminiscent of Gauss’s theorem in the space of Feynman diagrams.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoDavide Polvara's thesisMultipoint conformal blocks in conformal field theories2022-04-25T00:00:00+00:002022-04-25T00:00:00+00:00https://amplitudes.org/theses/Quintavalle<h1 id="multipoint-conformal-blocks-in-conformal-field-theories">Multipoint conformal blocks in conformal field theories</h1>
<h3 id="lorenzo-quintavalle">Lorenzo Quintavalle</h3>
<h2 id="link-to-pdf"><a href="/images/Lorenzo%20Quintavalle%20thesis.pdf">Link to PDF</a></h2>
<h2 id="abstract">Abstract</h2>
<p>A very powerful tool in Conformal Field Theories is the conformal block expansion, which plays a crucial role in the conformal bootstrap programme. The goal of this thesis is to improve the understanding and mathematical control over conformal block expansions for more than four external fields, studying the so-called multipoint conformal blocks from the perspective of the differential equations these satisfy. The results presented here stem from newly discovered relations between multipoint conformal blocks and Gaudin integrable models. These allow the introduction of special limits for multipoint conformal blocks which reduce them to some of their sub-components. Reduction to three-point blocks leads to a further novel connection between conformal blocks and integrable Calogero-Moser-Sutherland models. These results pave the way for future computations of multipoint conformal blocks, starting from certain well-behaved limits.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoLorenzo Quintavalle's thesisClosed. ~~A&I Group, Northwestern University~~2022-01-27T00:00:00+00:002022-01-27T00:00:00+00:00https://amplitudes.org/jobs/Northwestern<h1 id="postdoctoral-position-in-theoretical-physics">Postdoctoral Position in Theoretical Physics</h1>
<p>The <a href="http://fancyphysics.org">Amplitudes and Insights group</a> in the Department of Physics and Astronomy of Weinberg College of Arts and Sciences at Northwestern University welcomes applications for a postdoctoral research scholar to join the group beginning the autumn of 2021 with a focus on large-scale analytic prediction.</p>
<p>The posting shall remain open until the position is filled, however for full consideration, please apply by close of business on February 15, 2022.</p>
<p>What you will do:</p>
<ol>
<li>Apply amplitude insights to physical stories from particle physics, to gravitational wave physics, to cosmology.</li>
<li>Discover new structure in multi-loop gauge and gravity invariant predictions.</li>
<li>Provide technical leadership in large-scale analytic calculation, mentoring and supporting other members of the group.</li>
</ol>
<p>Required Qualifications: PhD in physics. Penchant for gauge invariance.</p>
<p>Highly Desired:</p>
<ul>
<li>Experience in calculating and analyzing the UV properties of multi-loop gauge and gravity scattering amplitudes, and associated automation.</li>
<li>Experience constructing representations manifesting the duality between color and kinematics in non-trivial gauge theories and double-copy construction in the color-dual web of theories.</li>
<li>Experience with the low-energy expansion of string predictions at tree and loop level.</li>
<li>Experience with classical gravitational wave calculation at higher order either in PN or PM expansions, preferably both.</li>
<li>Experience with scientific computing towards analytic results on high performance computing clusters.</li>
</ul>
<p>To Apply: This position is now closed. Please see <a href="http://amplitudes.org/jobs/">amplitudes.org</a> for any currently open positions.
<del>Applicants should send a CV with a list of publications and contact information for three references, as well as a scientific research statement of no greater than 4 pages</del></p>
<p><em>Northwestern University is an Equal Opportunity, Affirmative Action Employer of all protected classes, including veterans and individuals with disabilities. Women, underrepresented racial and ethnic minorities, individuals with disabilities, and veterans are encouraged to apply. Hiring is contingent upon eligibility to work in the United States.</em></p>John Joseph M. CarrascoPostdoc in hep-thCoherent states and classical radiative observables in the S-matrix formalism2022-01-01T00:00:00+00:002022-01-01T00:00:00+00:00https://amplitudes.org/theses/Gonzo<h1 id="coherent-states-and-classical-radiative-observables-in-the-s-matrix-formalism">“Coherent states and classical radiative observables in the S-matrix formalism”</h1>
<h3 id="riccardo-gonzos-thesis">Riccardo Gonzo’s thesis</h3>
<h2 id="link-to-pdf"><a href="/images/Riccardo%20Gonzo%20thesis.pdf">Link to PDF</a></h2>
<h2 id="summary">Summary</h2>
<p>In this thesis, we study classical radiative observables perturbatively in terms of on-shell scattering amplitudes. In particular, we focus primarily on the two-body problem in gauge and gravitational theories by using an effective field theory ap- proach. The Kosower-Maybee-O’Connell (KMOC) approach, which follows from the classical on-shell reduction of the in-in formalism by using appropriate massive particle wavefunctions, is extended to include classical waves which are naturally described by coherent states. Global observables like the impulse and localized observables like the waveform and gravitational event shapes are then studied in the amplitude approach, making contact also with asymptotic symmetries and light-ray operators defined near null infinity. The classical factorization of radiative observables from the uncertainty principle is proved to be equivalent to a Poisson distribution in the Fock space, and this provides new evidence in favor of a representation of the classical S-matrix in terms of an eikonal phase and a coherent state of gravitons.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoRiccardo Gonzo's thesisNon-planar anomalous dimensions in sYM theories2022-01-01T00:00:00+00:002022-01-01T00:00:00+00:00https://amplitudes.org/theses/Spiering<h1 id="non-planar-anomalous-dimensions-in-super-yang-mills-theories">Non-planar anomalous dimensions in super Yang-Mills theories.</h1>
<h3 id="anne-speiring">Anne Speiring</h3>
<h2 id="link-to-pdf"><a href="/images/Anne%20Spiering_Thesis.pdf">Link to PDF</a></h2>
<h2 id="summary">Summary</h2>
<p>Conformal supersymmetric Yang–Mills theories play an important role in the gauge-gravity correspondence and, despite being highly non-physical, have been a driving force for many new approaches in more realistic theories like QCD and gravity. An important class of objects in conformal field theories is the spectrum of scaling dimensions of local operators, specifically their non-trivial coupling-dependent parts, the anomalous dimensions. The discovery of integrability in planar maximally supersymmetric Yang–Mills theory led to considerable advances in the computation of its anomalous-dimension spectrum. Less is known at the non-planar level where the theory is assumed to be non-integrable. In this thesis we consider non-planar anomalous dimensions in conformal supersymmetric Yang–Mills theories with gauge group SU(N) and approach them by a number of means.</p>
<p>First, we use an on-shell form-factor approach based on the intimate connection between the dilatation operator and scattering amplitudes. The former gives rise to operator mixing and its diagonalisation gives the operators’ anomalous dimensions. The latter are basic observables in any quantum field theory, describing its interactions and linking theoretical developments to experimental investigations. A lot of progress has been made in recent years in the study of scattering amplitudes due to the advent of on-shell methods which circumvent many difficulties of more traditional approaches, and we use some of these here to extract the dilatation operator in certain sectors of the theories considered. In particular, we study a set of dimension-4 operators in N = 4 supersymmetric Yang–Mills theory that is relevant for the mixing of the theory’s on-shell Lagrangian, and compute the spectrum of non-planar anomalous dimensions in this sector. Furthermore, we extract the general form of the one-loop dilatation operator in the sector of purely scalar operators in the β-deformed version of this theory.</p>
<p>In the planar limit of the theories considered in this thesis, the dilatation operator maps to a spin-chain Hamiltonian that can be diagonalised by integrability techniques, in particular a suitable Bethe ansatz. In this mapping the spectrum of anomalous dimensions becomes the energy spectrum of the corresponding spin chains. When going away from the planar limit, integrability is lost, but we can compute non-planar corrections to the planar spectrum using Rayleigh–Schro ̈dinger perturbation theory.
Using the basis of Bethe states, we compute matrix elements of the deformed and undeformed dilatation operator relevant in this approach. We find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use nondegenerate perturbation theory to compute the leading 1/N^2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order.</p>
<p>Finally, we numerically study statistical properties of large sets of anomalous dimensions which we obtain from a direct diagonalisation of the dilatation operators discussed in this thesis. Specifically, we analyse the distribution of level spacings in these spectra and find universal features: in the planar limit it follows the Poisson distribution characteristic of integrable systems, and at finite values of N it transitions to the Wigner–Dyson distribution of the Gaussian orthogonal ensemble of random matrix theory. This provides numerical evidence that perturbative non-planar anomalous-dimension spectra are quantum-chaotic, which is further supported by similar findings in the spectral rigidity measuring long-range interactions in the spectra. We also demonstrate that the finite-N eigenvectors possess properties of chaotic states.</p>
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<p>Funded in part by the <a href="https://ec.europa.eu/programmes/horizon2020/">European Union’s Horizon 2020 Framework Program</a> under the Marie Skłodowska-Curie grant agreement No. 764850 (<a href="https://sagex.org">SAGEX</a>).</p>
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</table>John Joseph M. CarrascoAnne Spiering's thesis