Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop

TL;DR

This paper demonstrates that N=5 supergravity remains ultraviolet finite at four loops in four dimensions due to novel enhanced cancellations, challenging previous expectations based on symmetry arguments.

Contribution

It reveals the existence of nontrivial enhanced cancellations in four-loop amplitudes of N=5 supergravity, which are not apparent in traditional covariant formalisms.

Findings

Four-loop four-point amplitudes are ultraviolet finite in four dimensions.

Enhanced cancellations occur at three and four loops in N=4 and N=5 supergravity.

Standard methods and duality between color and kinematics were used to compute divergences.

Abstract

We show that the four-loop four-point amplitudes of N = 5 supergravity are ultraviolet finite in four dimensions, contrary to expectations based on supersymmetry and duality-symmetry arguments. We explain why the diagrams of any covariant local formalism cannot manifestly exhibit the necessary cancellations for finiteness but instead require a new type of nontrivial ultraviolet cancellation that we call "enhanced cancellations". We also show that the three-loop four-point amplitudes in N = 4 and N = 5 supergravity theories display enhanced cancellations. To construct the loop integrand, we use the duality between color and kinematics. We apply standard methods for extracting ultraviolet divergences in conjunction with the FIRE5 integral reduction program to arrive at the four-loop results.