Three-Loop Superfiniteness of N=8 Supergravity

TL;DR

This paper constructs the three-loop four-point amplitude of N=8 supergravity, showing it is ultraviolet finite in four dimensions due to novel cancellations, indicating potential perturbative finiteness of the theory.

Contribution

It demonstrates the three-loop four-point amplitude of N=8 supergravity is finite in four dimensions and uncovers cancellations beyond traditional expectations, suggesting all-loop finiteness.

Findings

Amplitude is ultraviolet finite in four dimensions.

Novel cancellations reduce divergence in D dimensions.

Potential all-loop perturbative finiteness of N=8 supergravity.

Abstract

We construct the three-loop four-point amplitude of N=8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions to be no worse than that of N=4 super-Yang-Mills theory -- a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N=8 supergravity may be a perturbatively finite theory of quantum gravity.