Gauging a Non-Semi-Simple WZW Model

TL;DR

This paper constructs and analyzes three-dimensional conformal sigma models from gauged WZW models based on a four-dimensional non-semi-simple group, revealing connections to black string solutions and flat spacetime via dualities.

Contribution

It introduces new 3D conformal sigma models from non-semi-simple gauged WZW models and explores their relation to black string solutions and flat spacetime through dualities.

Findings

Derived exact metric and dilaton fields for the models.

Established connection between axial gauging model and 3D black string.

Showed models can be mapped to flat spacetime via dualities.

Abstract

We consider gauged WZW models based on a four dimensional non-semi-simple group. We obtain conformal $\s$-models in $D=3$ spacetime dimensions (with exact central charge $c=3$) by axially and vectorially gauging a one-dimensional subgroup. The model obtained in the axial gauging is related to the $3D$ black string after a correlated limit is taken in the latter model. By identifying the CFT corresponding to these $\s$-models we compute the exact expressions for the metric and dilaton fields. All of our models can be mapped to flat spacetimes with zero antisymmetric tensor and dilaton fields via duality transformations.