Note on asymptotic symmetries and soft gluon theorems

TL;DR

The paper analyzes how soft gluon theorems relate to asymptotic symmetries in a matter-coupled non-Abelian gauge theory. It defines corresponding surface charges at null infinity and shows the leading soft gluon theorem emerges as a Ward identity of these asymptotic symmetries, incorporating both linear and non-linear charge actions. By adopting a simplified linearized setup with gluon-scalar interactions, it argues that the sub-leading soft gluon theorem can also arise from the same symmetry, though extending this to the full non-Abelian theory remains challenging. The work points to future directions, including handling all interaction vertices and multiple soft emissions within the asymptotic symmetry framework and clarifying the underlying algebraic structure.

Abstract

Recently, the leading soft gluon theorem with single soft emission was shown to be the Ward identity of a two dimensional $\cal G$-Kac-Moody symmetry. In this note, we show that the leading soft gluon theorem can be interpreted as the Ward identity for the asymptotic symmetries of non-Abelian gauge theory. We further argue that the sub-leading soft gluon theorem can follow from the same symmetry.