2D Kac-Moody symmetry of 4D Yang-Mills theory

Abstract

Scattering amplitudes of any four-dimensional theory with nonabelian gauge group $$ \mathcal{G} $$ may be recast as two-dimensional correlation functions on the asymptotic twosphere at null infinity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional $$ \mathcal{G} $$ -Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. The Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null infinity and comprise the four-dimensional asymptotic symmetry group.