Einstein-Yang-Mills theory : I. Asymptotic symmetries

TL;DR

This work analyzes the asymptotic symmetries of the Einstein–Yang–Mills system with or without a cosmological constant across $d$ dimensions. By applying a unified gauge-fixing and fall-off analysis, it shows that the residual symmetry algebra has a Virasoro–Kac–Moody type structure, extending known results from $d=3$ to $d=4$ asymptotically flat spacetimes. The authors then provide explicit descriptions of the asymptotic algebra in key cases, including $d\ge4$ AdS, higher-dimensional flat, 4D flat, and 3D AdS/flat settings, revealing a decomposition into a spacetime isometry part and a gauge-theory ideal, with the latter forming a generalized loop-like algebra on the sphere. This unified treatment clarifies how gravity and Yang–Mills sectors intertwine at infinity and lays groundwork for holographic current algebras and possible central extensions. The results advance understanding of how asymptotic symmetries organize in coupled gravitational and gauge systems and guide future holographic investigations.

Abstract

Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four dimensional asymptotically flat case.