Perturbative Quantum Gravity as a Double Copy of Gauge Theory

TL;DR

It is 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.

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.

Figures (2)

• Figure 1: The loop-level numerator identity enforced by the duality (\ref{['BCJDuality']}) on propagator $l_s$ of the left-most diagram equates that diagram's numerator with the sum of the numerators of the rightmost diagrams.
• Figure 2: Loop diagrams contributing to both ${{\cal N}=4}$ sYM and ${{\cal N}=8}$ sugra three-loop four-point amplitudes. Integrals (\ref{['LoopBCJ']}) are specified by combining their propagators with numerator factors given in table \ref{['NumeratorTable']}. The (internal) symmetry factor for diagram (d) is $S_{\rm (d)}=2$, the rest are unity. All distinct external permutations of each diagram contribute.