Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure

TL;DR

This paper demonstrates that the double-copy structure of gravity prevents divergences in half-maximal supergravity at specific loop orders and dimensions, linking these cancellations to properties of Yang-Mills theory.

Contribution

It reveals how the double-copy structure enforces finiteness in half-maximal supergravity at certain loops and dimensions, and provides explicit divergence forms.

Findings

No divergences at one loop in D<8 and two loops in D<6 for four and five points.

Explicit divergence forms at one loop in D=8 and two loops in D=6.

The cancellations are connected to forbidden color factors in Yang-Mills theory.

Abstract

We show that the double-copy structure of gravity forbids divergences in pure half-maximal (16 supercharge) supergravity at four and five points at one loop in D<8 and at two loops in D<6. We link the cancellations that render these supergravity amplitudes finite to corresponding ones that eliminate forbidden color factors from the divergences of pure nonsupersymmetric Yang-Mills theory. The vanishing of the two-loop four-point divergence in D=5 half-maximal supergravity is an example where a valid counterterm satisfying the known symmetries exists, yet is not present. We also give explicit forms of divergences in half-maximal supergravity at one loop in D=8 and at two loops in D=6.