Nilpotent Gauging of SL(2,R)$WZNW$ models, and Liouville Field

TL;DR

This paper explores how gauging specific subgroups of SL(2,R) WZNW models simplifies the models to Liouville theory or black string solutions, revealing connections through gauge group transformations.

Contribution

It demonstrates the reduction of SL(2,R) WZNW models to Liouville theory and black string solutions via nilpotent gauging and subgroup extensions, highlighting gauge group boosting.

Findings

Gauging E(1) subgroup yields Liouville field theory.

Gauging E(1)×U(1) produces extremal black string solutions.

Solutions relate to known black hole and black string models through gauge transformations.

Abstract

We consider the gauging of $ SL(2,R) $ WZNW model by its nilpotent subgroup E(1). The resulting space-time of the corresponding sigma model is seen to collapse to a one dimensional field theory of Liouville. Gauging the diagonal subgroup $ E(1) \times U(1) $ of $SL(2,R) \times U(1)$ theory yields an extremal three dimensional black string. We show that these solutions are obtained from the two dimensional black hole of Witten and the three dimensional black string of Horne and Horowitz by boosting the gauge group.