Charge algebra for non-abelian large gauge symmetries at $O(r)$

TL;DR

This paper extends the understanding of asymptotic symmetries in Yang-Mills theory by incorporating $O(r)$ gauge parameters, leading to a well-defined charge algebra that captures subleading infrared behaviors.

Contribution

It introduces a relaxed asymptotic field behavior compatible with $O(r)$ gauge symmetries, enabling a consistent charge algebra in non-abelian gauge theories.

Findings

Extended space admits a symplectic structure with well-defined charges.

Poisson brackets reproduce the symmetry algebra.

Compatible with subleading infrared behaviors in Yang-Mills theory.

Abstract

Asymptotic symmetries of gauge theories are known to encode infrared properties of radiative fields. In the context of tree-level Yang-Mills theory, the leading soft behavior of gluons is captured by large gauge symmetries with parameters that are $O(1)$ in the large $r$ expansion towards null infinity. This relation can be extended to subleading order provided one allows for large gauge symmetries with $O(r)$ gauge parameters. The latter, however, violate standard asymptotic field fall-offs and thus their interpretation has remained incomplete. We improve on this situation by presenting a relaxation of the standard asymptotic field behavior that is compatible with $O(r)$ gauge symmetries at linearized level. We show the extended space admits a symplectic structure on which $O(1)$ and $O(r)$ charges are well defined and such that their Poisson brackets reproduce the corresponding symmetry algebra.