Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

TL;DR

This paper derives new one-loop gravity scattering amplitudes using gauge theory relations, specifically employing KLT relations to connect gravity and gauge theory amplitudes, extending known results to all n for certain helicity configurations.

Contribution

It introduces two infinite sequences of one-loop n-graviton amplitudes in supergravity and gravity with matter, derived from gauge theory relations and unitarity cuts, extending previous results.

Findings

Explicit all-plus gravity amplitudes for n<7 derived from unitarity cuts.

Extended KLT relations connect gauge theory and gravity amplitudes.

Soft and collinear properties used to infer amplitudes for all n.

Abstract

By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the `maximally helicity-violating' amplitudes in N=8 supergravity, and the `all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n < 7, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found `dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N=4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n < 7 N=8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations.