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.