Asymptotic symmetries of Yang-Mills theory

Abstract

Asymptotic symmetries at future null infinity ( $$ \mathrm{\mathcal{I}} $$ +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through $$ \mathrm{\mathcal{I}} $$ + 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 $$ \mathrm{\mathcal{I}} $$ + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of $$ \mathrm{\mathcal{I}} $$ +. The current Ward identities include Weinberg’s soft photon theorem and its colored extension.