Gauging of Lorentz Group WZW Model by its Null Subgroup

TL;DR

This paper explores the gauging of the Lorentz group in a WZW model by its null subgroup, revealing connections to Liouville and Toda theories through effective actions and subgroup limits.

Contribution

It introduces a novel analysis of Lorentz group WZW models gauged by null and Euclidean subgroups, linking them to Liouville and Toda theories.

Findings

Effective action describes a bosonic field with external charge

Large boost limit yields Toda theory interpretation

Generalized bilinear form leads to new gauge theories

Abstract

We consider the standard vector gauging of Lorentz group $ SO(3,1) $ WZW model by its non-semisimple null Euclidean subgroup in two dimensions $ E(2) $. The resultant effective action of the theory is seen to describe a one dimensional bosonic field in the presence of external charge that we interpret it as a Liouville field. Gauging a boosted $ SO(3) $ subgroup, we find that in the limit of the large boost, the theory can be interpreted as an interacting Toda theory. We also take the generalized non-standard bilinear form for $SO(3,1) $ and gauge both $ SO(3) $ and $E(2)$ subgroups and discuss the resultant theories.