On Free Field Realizations of Strings in BTZ

TL;DR

This paper explores free field realizations of the SL(2,R) current algebra in the context of BTZ black holes, extending previous work to include discrete representations and interpreting spectral flow as field twisting.

Contribution

It introduces a new free scalar field realization for principal discrete representations of SL(2,R) and connects spectral flow to field twisting, expanding the understanding of string descriptions in BTZ backgrounds.

Findings

Realizations correspond to principal discrete and continuous representations.

Spectral flow interpreted as twisting of free scalar fields.

Connections established between realizations and BTZ Lagrangian.

Abstract

We discuss realizations of the SL(2,R) current algebra in the hyperbolic basis using free scalar fields. It has been previously shown by Satoh how such a realization can be used to describe the principal continuous representations of SL(2,R). We extend this work by introducing another realization that corresponds to the principal discrete representations of SL(2,R). We show that in these realizations spectral flow can be interpreted as twisting of a free scalar field. Finally, we discuss how these realizations can be obtained from the BTZ Lagrangian.