Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity

TL;DR

This paper demonstrates that the U(1) anomaly in N=4 supergravity's one-loop scattering amplitudes can be canceled with a finite local counterterm, impacting the understanding of ultraviolet divergences in the theory.

Contribution

It provides a detailed method to cancel the U(1) anomaly at one loop using a finite counterterm, affecting the analysis of ultraviolet divergences.

Findings

Anomalous amplitudes can be set to zero with a finite counterterm.

The counterterm also cancels evanescent contributions in dimensional regularization.

Reanalysis of four-loop divergences is necessary after this cancellation.

Abstract

${{\cal N}=4}$ supergravity is understood to contain a $U(1)$ anomaly which manifests itself via the nonvanishing of loop-level scattering amplitudes that violate a tree-level charge conservation rule. In this letter we provide detailed evidence that at one loop such anomalous amplitudes can be set to zero by the addition of a finite local counterterm. We show that the same counterterm also cancels evanescent contributions which play an important role in the analysis of ultraviolet divergences in dimensionally regularized gravity. These cancellations call for a reanalysis of the four-loop ultraviolet divergences previously found in this theory without the addition of such counterterms.