One-Loop n-Point Helicity Amplitudes in (Self-Dual) Gravity

TL;DR

This paper proposes a general ansatz for one-loop all-plus helicity graviton amplitudes in Einstein gravity, validated against explicit computations and exhibiting correct physical behavior, with connections to self-dual gravity and Yang-Mills theory.

Contribution

It introduces a universal ansatz for one-loop n-point all-plus helicity graviton amplitudes in Einstein gravity, matching explicit calculations for up to six points and capturing key physical limits.

Findings

Ansatz agrees with explicit unitarity cut computations for n ≤ 6

Amplitudes exhibit correct soft and collinear limits

Results relate to self-dual gravity and Yang-Mills amplitudes

Abstract

We present an ansatz for all one-loop amplitudes in pure Einstein gravity for which the n external gravitons have the same outgoing helicity. These loop amplitudes, which are rational functions of the momenta, also arise in the quantization of self-dual gravity in four-dimensional Minkowski space. Our ansatz agrees with explicit computations via D-dimensional unitarity cuts for n less than or equal to 6. It also has the expected analytic behavior, for all n, as a graviton becomes soft, and as two momenta become collinear. The gravity results are closely related to analogous amplitudes in (self-dual) Yang-Mills theory.