Dynamical Edge Modes in Yang-Mills Theory

TL;DR

This paper investigates the boundary dynamics of Yang-Mills theory, revealing that bulk and edge degrees of freedom are inherently coupled due to the non-abelian gauge structure, with implications for understanding gauge theories with boundaries.

Contribution

It introduces a decomposition of fields that separates bulk and edge symplectic forms and demonstrates their intrinsic coupling in non-abelian Yang-Mills theory.

Findings

Bulk and edge symplectic sectors are coupled in Yang-Mills theory.

Dynamical edge modes extend Maxwell boundary conditions to non-abelian cases.

Coupling persists in weak-field and horizon limits.

Abstract

We study the symplectic structure and dynamics of Yang-Mills theory in the presence of a boundary. We introduce a decomposition of the fields on a Cauchy slice such that the symplectic form splits cleanly into independent bulk and edge parts. However, we find that the dynamics inherently couples these two symplectic sectors, a feature arising from the non-abelian nature of the gauge group. This is shown by extending to Yang-Mills theory the dynamical edge mode boundary condition recently introduced in Maxwell theory. We finish with analyses of the weak-field expansion and the horizon limit, finding in the latter case that the dynamical interplay between bulk and edge degrees of freedom persists.