Analytical Solution of the SL(2,R)/U(1) WZNW Black Hole Model

TL;DR

This paper provides an exact analytical solution to the SL(2,R)/U(1) WZNW black hole model, revealing its integrable structure and paving the way for canonical quantization.

Contribution

It introduces a Lax pair, Bäcklund transformation, and differential equations defining the model's structure, offering new insights into its integrability and solution space.

Findings

Lax pair representation established for the model

A Bäcklund transformation derived

General solutions described via Gelfand-Dikii type equations

Abstract

The gauged SL(2,R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. We have found a Lax pair representation for the non-linear equations of motion, and a B"acklund transformation. A second-order differential equation of the Gelfand-Dikii type defines the Poisson bracket structure of the theory, and its fundamental solutions describe the general solution of the WZNW model as well. The physical and free fields are related by non-local transformations. The (anti-)chiral component of the energy-momentum tensor which factorizes into conserved quantities satisfying a non-linear algebra characteristic for parafermions assumes the expected canonical free field form. So the black hole model seems to be prepared for an exact canonical quantization.