# Classical Gravity from Gluon Interactions

### Canxin Shi

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## Abstract

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.

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.

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.

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.

Funded in part by the European Union’s Horizon 2020 Framework Program under the Marie Skłodowska-Curie grant agreement No. 764850 (SAGEX).