Integration of the SL(2,R)/U(1) Gauged WZNW Model with Periodic Boundary Conditions

TL;DR

This paper extends the classical ext{SL}(2,R)/U(1) gauged WZNW model to include periodic boundary conditions, analyzing its Poisson structure and preparing for quantization in curved string backgrounds.

Contribution

It introduces a method to incorporate periodic boundary conditions into the classical ext{SL}(2,R)/U(1) gauged WZNW model and computes its Poisson brackets considering zero modes.

Findings

Poisson bracket structure differs from previous calculations due to zero modes.

Physical fields can be transformed into canonical free fields for quantization.

Provides groundwork for exact canonical quantization of the model.

Abstract

Gauged WZNW models are integrable conformal field theories. We integrate the classical \slu{} theory with periodic boundary conditions, which describes closed strings moving in a curved target-space geometry. We calculate its Poisson bracket structure by solving an initial state problem. The results differ from previous field-theoretic calculations due to zero modes. For a future exact canonical quantization the physical fields are (non-locally) transformed onto canonical free fields.