Canonical quantization of the boundary Wess-Zumino-Witten model

TL;DR

This paper analyzes the canonical structure of the boundary WZW model, revealing its phase space equivalence with Chern-Simons theory on a solid cylinder with Wilson lines, and offers a quantization approach linking boundary conformal field theories to topological theories.

Contribution

It establishes a detailed canonical analysis of the boundary WZW model and connects it to Chern-Simons theory, providing a new perspective on their relationship and a method for quantization.

Findings

Phase space of boundary WZW matches Chern-Simons on a solid cylinder with Wilson lines.

Decomposition of Chern-Simons phase space facilitates quantization.

Provides a quantization scheme for the boundary WZW model.

Abstract

We present an analysis of the canonical structure of the WZW theory with untwisted conformal boundary conditions. The phase space of the boundary theory on a strip is shown to coincide with the phase space of the Chern-Simons theory on a solid cylinder (a disc times a line) with two Wilson lines. This reveals a new aspect of the relation between two-dimensional boundary conformal field theories and three-dimensional topological theories. A decomposition of the Chern-Simons phase space on a punctured disc in terms of the one on a punctured sphere and of coadjoint orbits of the loop group easily lends itself to quantization, providing at the same time a quantization of the boundary WZW model.