On the U(1) duality anomaly and the S-matrix of N=4 supergravity

TL;DR

This paper investigates the U(1) duality anomaly in N=4 supergravity, deriving its origin from superconformal formulations, and explores how it affects the quantum S-matrix, revealing symmetry-breaking effects at one-loop level.

Contribution

It introduces a novel derivation of the U(1) anomaly in N=4 supergravity using superconformal methods and analyzes its impact on the one-loop S-matrix through explicit amplitude calculations.

Findings

U(1) symmetry is broken at the quantum level in N=4 supergravity.

New one-loop amplitudes with non-vanishing soft-scalar limits are found.

The anomaly is related to specific local and nonlocal terms in the effective action.

Abstract

N=4 Poincare supergravity has a global SU(1,1) duality symmetry that acts manifestly only on shell as it involves duality rotations of vector fields. A U(1) subgroup of this symmetry is known to be anomalous at the quantum level in the presence of a non-trivial gravitational background. We first derive this anomaly from a novel perspective, by relating it to a similar anomaly in conformal supergravity where SU(1,1) acts off shell, using the fact that N=4 Poincare supergravity has a superconformal formulation. We explicitly construct the corresponding local and nonlocal anomalous terms in the one-loop effective action. We then study how this anomaly is reflected in the supergravity S-matrix. Calculating one-loop N=4 supergravity scattering amplitudes (with and without additional matter multiplets) using color/kinematics duality and the double-copy construction we find that a particular U(1) symmetry which was present in the tree-level amplitudes is broken at the quantum level. This breaking manifests itself in the appearance of new one-loop N=4 supergravity amplitudes that have non-vanishing soft-scalar limits (these amplitudes are absent in N>4 supergravities). We discuss the relation between these symmetry-violating amplitudes and the corresponding U(1) anomalous term in the one-loop supergravity effective action.