Canonical quantization of the WZW model with defects and Chern-Simons theory

TL;DR

This paper establishes a deep connection between the phase space of the WZW model with defects and the phase space of Chern-Simons theory with Wilson lines, providing a canonical quantization framework for these models.

Contribution

It demonstrates symplectomorphisms between the phase spaces of WZW models with defects and Chern-Simons theories with Wilson lines, extending the understanding of their geometric and topological relations.

Findings

Established symplectomorphism between WZW model with N defects and Chern-Simons theory with Wilson lines.

Connected phase space of WZW model with boundary conditions to Chern-Simons theory on sphere with holes.

Provided a canonical quantization approach for models with defects and branes.

Abstract

We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with $N$ defects on cylinder and phase space of Chern-Simons theory on annulus times $R$ with $N$ Wilson lines, and between phase space of WZW model with $N$ defects on strip and Chern-Simons theory on disc times $R$ with $N+2$ Wilson lines. We obtained also symplectomorphism between phase space of the $N$-fold product of the WZW model with boundary conditions specified by permutation branes, and phase space of Chern-Simons theory on sphere with $N$ holes and two Wilson lines.