Is N = 8 Supergravity Ultraviolet Finite?

TL;DR

This paper explores the possibility that N=8 supergravity in four dimensions might be ultraviolet finite, challenging traditional power counting by leveraging recent one-loop amplitude cancellations and unitarity methods.

Contribution

It proposes that higher-loop cancellations in N=8 supergravity suggest potential ultraviolet finiteness, supported by unitarity-based evidence and extending one-loop findings.

Findings

One-loop N=8 supergravity amplitudes satisfy the no-triangle hypothesis.

Higher-loop evidence indicates similar divergence behavior to N=4 super-Yang-Mills.

Potential for ultraviolet finiteness in four dimensions is discussed with feasible calculations.

Abstract

Conventional wisdom holds that no four-dimensional gravity field theory can be ultraviolet finite. This understanding is based mainly on power counting. Recent studies confirm that one-loop N = 8 supergravity amplitudes satisfy the so-called `no-triangle hypothesis', which states that triangle and bubble integrals cancel from these amplitudes. A consequence of this hypothesis is that for any number of external legs, at one loop N = 8 supergravity and N = 4 super-Yang-Mills have identical superficial degrees of ultraviolet behavior in D dimensions. We describe how the unitarity method allows us to promote these one-loop cancellations to higher loops, suggesting that previous power counts were too conservative. We discuss higher-loop evidence suggesting that N = 8 supergravity has the same degree of divergence as N = 4 super-Yang-Mills theory and is ultraviolet finite in four dimensions. We comment on calculations needed to reinforce this proposal, which are feasible using the unitarity method.