# Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity

## TL;DR

This paper investigates one-loop amplitudes in N=4 supergravity, revealing how evanescent operators and U(1) anomalies are interconnected, with implications for understanding divergences in the theory.

## Contribution

It introduces a gauge-invariant tensor basis for analyzing supergravity amplitudes and uncovers the link between evanescent effects and U(1) anomalies.

## Key findings

- Evanescent operators are linked to supersymmetric curvature-squared completions.
- U(1) anomalies are intertwined with evanescent contributions in one-loop amplitudes.
- Provides tensor bases and projectors useful for Yang--Mills and supergravity analyses.

## Abstract

We evaluate one-loop amplitudes of N = 4 supergravity in D dimensions using the double-copy procedure that expresses gravity integrands in terms of corresponding ones in Yang--Mills theory.We organize the calculation in terms of a set of gauge-invariant tensors, allowing us to identify evanescent contributions. Among the latter, we find the matrix elements of supersymmetric completions of curvature-squared operators. In addition, we find that such evanescent terms and the U(1)-anomalous contributions to one-loop N = 4 amplitudes are tightly intertwined. The appearance of evanescent operators in N = 4 supergravity and their relation to anomalies raises the question of their effect on the known four-loop divergence in this theory. We provide bases of gauge-invariant tensors and corresponding projectors useful for Yang--Mills theories as a by-product of our analysis.