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

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.

10 pages, LaTeX, amsfonts; one reference added

References in corpus (4)

• Effective action of gauged WZW model and exact string solutions
• Black Holes from Non-Abelian Toda Theories
• Non Abelian Toda Theory : A Completely Integrable Model for Strings on a Black Hole Background
• Folded Strings Falling into a Black Hole

Cited by in corpus (5)

• Classification of Standard-like Heterotic-String Vacua
• FZZ Scattering
• Integration of the SL(2,R)/U(1) Gauged WZNW Model with Periodic Boundary Conditions
• Exact Operator Quantization of the Euclidean Black Hole CFT
• Singular Liouville fields and spiky strings in $\rr^{1,2}$ and $SL(2,\rr)$