Systematics of Boundary Actions in Gauge Theory and Gravity

TL;DR

This paper systematically studies boundary modes in gauge and gravity theories, developing techniques to compute boundary actions that encode the dynamics dictated by asymptotic symmetries, with applications to AdS$_3$ gravity.

Contribution

It introduces new methods for isolating boundary modes and their dynamics in gauge and gravitational theories, enhancing understanding of boundary actions and asymptotic symmetries.

Findings

Developed approaches for extracting boundary modes in covariant phase space

Applied techniques to AdS$_3$ gravity with various boundary conditions

Demonstrated how boundary actions encode conserved current correlations

Abstract

We undertake a general study of the boundary (or edge) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the corresponding boundary action. Such actions capture all the dynamics of the system that are implied by its asymptotic symmetry group, such as correlation functions of the corresponding conserved currents. Working in the covariant phase space formalism, we develop a collection of approaches for isolating the boundary modes and their dynamics, and illustrate with various examples, notably AdS$_3$ gravity (with and without a gravitational Chern-Simons terms) subject to assorted boundary conditions.