Remarks on free field realization of SL(2,R)/U(1) x U(1) WZNW model

TL;DR

This paper develops free field representations for the SL(2,R)/U(1) x U(1) WZNW model using a twisted Bershadsky-Kutasov approach, revealing spectral flow identities and matching correlation functions with sine-Liouville theory.

Contribution

It introduces a novel free field realization for the model and demonstrates spectral flow identities, connecting to sine-Liouville theory results.

Findings

Derived free field representations for the model.

Identified spectral flow symmetry identities.

Established exact agreement of correlation functions with sine-Liouville theory.

Abstract

Free field representations of vertex algebra in SL(2,R)/U(1) x U(1) WZNW model are constructed by considering a twisted version of the Bershadsky-Kutasov free field description of discrete states in the two-dimensional black hole CFT. These correspond to conjugate representations describing primary states in the model on SL(2,R)/U(1) x U(1). A particular evaluation of these leads to identities due to the spectral flow symmetry of sl(2)_k algebra. The computation of correlation functions is discussed and, as an application, these are compared with analogous results known for the sine-Liouville theory. Exact agreement is observed between both analytic structures.