N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops

TL;DR

This paper computes two-loop four-graviton scattering amplitudes in various supergravity theories using the double-copy structure derived from gauge theory, revealing their infrared behavior and providing compact finite remainders.

Contribution

It presents the first complete two-loop four-graviton amplitudes for N=4,5,6 supergravity using the color-kinematics duality and double-copy approach, including the N=8 case.

Findings

Two-loop divergences match the squares of one-loop amplitudes.

Finite remainders are expressed in compact forms, with a simple symbol for N=8.

Results confirm the infrared behavior predicted by theory.

Abstract

We present the full two-loop four-graviton amplitudes in N=4,5,6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N=0,1,2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N=8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.