Asymptotic Symmetries of Yang-Mills Theory

TL;DR

This paper investigates the asymptotic symmetries of Yang-Mills theories at null infinity, proposing an infinite-dimensional symmetry group including a G Kac-Moody algebra, and connects these symmetries to soft theorems.

Contribution

It conjectures the inclusion of a G Kac-Moody symmetry in the asymptotic structure of Yang-Mills theories and constructs the associated currents from boundary gauge fields.

Findings

Symmetry group is infinite-dimensional, including a G Kac-Moody algebra.

Constructed Kac-Moody currents from boundary gauge fields.

Derived Ward identities that encompass Weinberg's soft photon theorem.

Abstract

Asymptotic symmetries at future null infinity (I+) of Minkowski space for electrodynamics with massless charged fields, as well as non-Abelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through I+ suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at I+ and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of I+. The current Ward identities include Weinberg's soft photon theorem and its colored extension.