2D Kac-Moody Symmetry of 4D Yang-Mills Theory

TL;DR

This paper reveals that scattering amplitudes in 4D Yang-Mills theory can be expressed as 2D correlation functions, with the soft gluon theorem corresponding to a Kac-Moody Ward identity, unveiling a new 2D symmetry structure.

Contribution

It demonstrates that the soft gluon theorem in 4D Yang-Mills theory is equivalent to a holomorphic Kac-Moody symmetry acting at null infinity, connecting 4D gauge symmetries to 2D current algebras.

Findings

Scattering amplitudes are recast as 2D correlation functions.

Soft gluon theorem corresponds to a Kac-Moody Ward identity.

Identifies a 2D Kac-Moody symmetry as part of the 4D asymptotic symmetry group.

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 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.