Anomaly and double copy in quantum self-dual Yang-Mills and gravity

TL;DR

This paper investigates quantum anomalies and a novel double copy structure in self-dual Yang-Mills and gravity, revealing quantum corrections to symmetries and a new double copy relation for loop amplitudes.

Contribution

It demonstrates how classical symmetries are quantum corrected in self-dual theories and uncovers a new BCJ-like double copy for loop-integrated amplitudes.

Findings

Quantum corrections to classical symmetries due to anomalies.

Quantum-corrected light-cone Lagrangians consistent with amplitude simplicity.

Discovery of a BCJ-like double copy for loop-integrated amplitudes.

Abstract

Recent works have explored how scattering amplitudes in quantum self-dual Yang-Mills theory and self-dual gravity can be interpreted as resulting from an anomaly, as first proposed by W. Bardeen. We study this problem in the light-cone-gauge formulation of the theories. Firstly, we describe how the infinite tower of symmetries associated to classical integrability can be quantum corrected, exhibiting the one-loop anomaly. Secondly, we present quantum-corrected light-cone Lagrangians worthy of the simplicity of the amplitudes, building on recent works describing the anomaly in twistor space. Finally, we discover an unexpected BCJ-like double copy for the (loop-integrated) amplitudes, distinct from the well-known BCJ double copy for the loop integrands.