Asymptotic Structure of Higher Dimensional Yang-Mills Theory

TL;DR

This paper develops a unified covariant phase space formalism for higher-dimensional non-Abelian gauge theories, revealing the structure of edge modes, soft gluon theorems, and their algebraic properties in arbitrary dimensions.

Contribution

It introduces a unified approach to the phase space of higher-dimensional Yang-Mills theories, including edge modes and shadow transform techniques, connecting symplectic structure to soft theorems.

Findings

Unified treatment of symplectic form in odd and even dimensions

Derivation of the algebra of the vacuum sector of the Hilbert space

Leading soft gluon theorem in higher dimensions

Abstract

Using the covariant phase space formalism, we construct the phase space for non-Abelian gauge theories in $(d+2)$-dimensional Minkowski spacetime for any $d \geq 2$, including the edge modes that symplectically pair to the low energy degrees of freedom of the gauge field. Despite the fact that the symplectic form in odd and even-dimensional spacetimes appear ostensibly different, we demonstrate that both cases can be treated in a unified manner by utilizing the shadow transform. Upon quantization, we recover the algebra of the vacuum sector of the Hilbert space and derive a Ward identity that implies the leading soft gluon theorem in $(d+2)$-dimensional spacetime.