The Ultraviolet Properties of N=4 Supergravity at Four Loops

TL;DR

This paper shows that pure N=4 supergravity exhibits a four-loop ultraviolet divergence, likely caused by a duality-symmetry anomaly, marking the first such divergence in a pure ungauged supergravity in four dimensions.

Contribution

It provides the first explicit calculation of a four-loop divergence in pure N=4 supergravity, linking it to a duality-symmetry anomaly using color-kinematics duality.

Findings

Ultraviolet divergence identified at four loops

Divergence attributed to duality-symmetry anomaly

First such divergence in pure ungauged supergravity in 4D

Abstract

We demonstrate that pure N=4 supergravity is ultraviolet divergent at four loops. The form of the divergence suggests that it is due to the rigid U(1) duality-symmetry anomaly of the theory. This is the first known example of an ultraviolet divergence in a pure ungauged supergravity theory in four dimensions. We use the duality between color and kinematics to construct the integrand of the four-loop four-point amplitude, whose ultraviolet divergence is then extracted by standard integration techniques.