Perturbative gauge theory at null infinity

TL;DR

This work constructs a two-dimensional CFT whose target is the complexified null boundary $\mathscr{I}_{\mathbb{C}}$ of four-dimensional Minkowski space, hosting radiative Yang–Mills states. A Kac–Moody current action yields Ward identities for large gauge transformations that reproduce the leading soft gluon theorem, while charges acting as sphere vector fields generate the subleading soft gluon theorem; boundary correlators reproduce the full tree-level YM S-matrix in the single-trace sector. The model also includes non-unitary gravitational degrees of freedom, interpreted as non-minimal conformal gravity related to twistor-string theories, which mediate multi-trace amplitudes. Together, these results present a perturbative boundary description of gauge theory at null infinity, linking soft theorems, asymptotic symmetries, and twistor/ambitwistor formalisms within a flat-space holographic-like framework.

Abstract

We describe a theory living on the null conformal boundary of four-dimensional Minkowski space, whose states include the radiative modes of Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic 'large' gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of the boundary. Correlation functions of the Yang-Mills states are shown to produce the full classical S-matrix of Yang-Mills theory. The model contains additional states arising from non-unitary gravitational degrees of freedom, indicating a relationship with the twistor-string of Berkovits & Witten.