Asymptotic Symmetries in $(d+2)$-Dimensional Gauge Theories

TL;DR

This work extends the soft theorem–Ward identity correspondence for gauge theories to all $(d+2)$-dimensional spacetimes, showing that the subleading soft photon theorem corresponds to a Ward identity for divergent large U(1) gauge transformations at null infinity, while the leading and subleading soft gluon theorems correspond to analogous Ward identities in non-Abelian theories. The authors implement antipodal matching of radiative and Coulombic data on null infinity and employ a covariant phase-space framework to define charges decomposed into soft and hard parts, including divergent contributions that cancel appropriately. The results hold for both even and odd dimensions and rely on a systematic extension from abelian to non-Abelian gauge theories, with explicit expressions for the Ward identities and their relation to soft factors. Overall, the paper clarifies the asymptotic symmetry content of massless gauge theories across dimensions and demonstrates the universal role of divergent large gauge transformations in encoding subleading soft behavior.

Abstract

We show that the subleading soft photon theorem in a $(d+2)$-dimensional massless abelian gauge theory gives rise to a Ward identity corresponding to divergent large gauge transformations acting on the celestial sphere at null infinity. We further generalize our analysis to $(d+2)$-dimensional non-abelian gauge theories and show that the leading and subleading soft gluon theorem give rise to Ward identities corresponding to asymptotic symmetries of the theory.