Boundary WZW, G/H, G/G and CS theories

TL;DR

This paper analyzes the canonical structure of boundary and bulk coset models, revealing their phase spaces correspond to double Chern-Simons theories, and provides an explicit canonical description of boundary G/G coset theory, facilitating its quantization.

Contribution

It extends the canonical analysis of WZW and coset models to boundary cases, connecting them with double Chern-Simons theories and explicitly describing the boundary G/G coset structure.

Findings

Phase spaces of coset theories match double Chern-Simons theories.

Explicit canonical structure of boundary G/G coset theory obtained.

Boundary G/G coset theory can be quantized as a topological field theory.

Abstract

We extend the analysis of the canonical structure of the Wess-Zumino-Witten theory to the bulk and boundary coset G/H models. The phase spaces of the coset theories in the closed and in the open geometry appear to coincide with those of a double Chern-Simons theory on two different 3-manifolds. In particular, we obtain an explicit description of the canonical structure of the boundary G/G coset theory. The latter may be easily quantized leading to an example of a two-dimensional topological boundary field theory.