  Scattering amplitudes of any four-dimensional theory with nonabelian gauge
group $\mathcal G$ may be recast as two-dimensional correlation functions on
the asymptotic two-sphere 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.
