On the Boundary Dynamics of Chern-Simons Gravity

TL;DR

This paper investigates boundary dynamics in Chern-Simons gravity, deriving boundary actions as WZW models with gauge invariance, applicable to (E/A)dS spacetimes, and clarifies their properties and relations to existing theories.

Contribution

It provides a covariant, gauge-invariant derivation of boundary actions for Chern-Simons gravity, establishing their form as WZW models with specific target spaces.

Findings

Boundary actions are WZW models with (E/A)dS target spaces.

The derivation is fully covariant and gauge invariant.

Results connect to and clarify existing boundary theories in gravity.

Abstract

We study Chern-Simons theory with a complex G_C or a real G x G gauge group on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a G_C/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, for (E/A)dS gravity, the boundary action is a WZW model with target space (E/A)dS_3, reminiscent of a worldsheet for worldsheet mechanism. We discuss in some detail the properties of the boundary theories that arise and we confront our results with various related constructions in the literature.