Edge Dynamics from the Path Integral: Maxwell and Yang-Mills

TL;DR

This paper derives a canonical edge action for gauge theories like Maxwell and Yang-Mills using the path integral, enabling analysis of boundary dynamics and correlators in various spacetime settings.

Contribution

It introduces a unified derivation of edge actions for gauge theories via the path integral, connecting boundary correlators with particle-on-a-group models.

Findings

Recovered Maxwell edge dynamics in Rindler space

Identified boundary action as particle-on-a-group in 2d Yang-Mills

Matched Wilson line correlators with bilocal operators

Abstract

We derive an action describing edge dynamics on interfaces for gauge theories (Maxwell and Yang-Mills) using the path integral. The canonical structure of the edge theory is deduced and the thermal partition function calculated. We test the edge action in several applications. For Maxwell in Rindler space, we recover earlier results, now embedded in a dynamical canonical framework. A second application is 2d Yang-Mills theory where the boundary action becomes just the particle-on-a-group action. Correlators of boundary-anchored Wilson lines in 2d Yang-Mills are matched with, and identified as correlators of bilocal operators in the particle-on-a-group edge model.