Perturbative Quantum Gravity as a Double Copy of Gauge Theory

TL;DR

This paper explores the extension of the color-kinematics duality to all quantum loop orders, enabling the construction of gravity amplitudes from gauge theory, demonstrated through multiloop examples including supergravity.

Contribution

It conjectures that the color-kinematics duality applies at all loop levels and shows how to derive gravity amplitudes from gauge theory using double copies, with explicit multiloop tests.

Findings

Three-loop four-point N=4 super-Yang-Mills amplitude satisfies the duality.

Double copy yields N=8 supergravity amplitude from gauge theory.

Two-loop non-supersymmetric test produces gravity coupled to matter fields.

Abstract

In a previous paper we observed that (classical) tree-level gauge theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N = 4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N = 8 supergravity. We also remark on a non-supersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an anti-symmetric tensor and dilaton.