Asymptotic Higher Spin Symmetries IV: Einstein-Yang-Mills Theory

TL;DR

This paper extends the analysis of asymptotic higher spin symmetries to Einstein-Yang-Mills theory, revealing an infinite set of conserved charges and a generalized celestial algebra structure.

Contribution

It introduces a new framework for higher spin symmetries in Einstein-Yang-Mills theory, including the construction of conserved charges and a generalized symmetry algebra.

Findings

Existence of symmetry parameters satisfying dual equations of motion.

Construction of an infinite collection of conserved charges.

Generalization of the celestial $sw_{1+ Infty}$ algebra with a consistent symmetry bracket.

Abstract

We generalize the analysis of the asymptotic higher spin symmetries developed in the first three parts of this series by considering the minimal coupling of Einstein Gravity and Yang-Mills theory. We show that there exist symmetry parameters that satisfy a collection of dual equations of motion, which allow the construction of an infinite collection of charges that are conserved in the absence of radiation. These Noether charges act on the Einstein Yang-Mills phase space canonically and non-linearly. Their action defines a symmetry algebroid which reduces to a symmetry algebra at non-radiative cuts and generalizes the celestial $sw_{1+\infty}$ algebra. The corresponding symmetry bracket is shown to satisfy the Jacobi identity and an interesting cross-product structure, which is analyzed in details.