Four Point Functions in the SL(2,R) WZW Model

TL;DR

This paper computes four-point functions in the SL(2,R) WZW model, analyzing spectral flow sectors and providing leading order expansions, with consistency checks on related three-point functions.

Contribution

It presents the first detailed calculation of winding conserving four-point functions in arbitrary spectral flow sectors of the SL(2,R) WZW model.

Findings

Derived leading order expansions of four-point functions in both m- and x-bases.

Performed consistency checks on three-point functions involving spectral flow.

Extended understanding of correlation functions in the SL(2,R) WZW model.

Abstract

We consider winding conserving four point functions in the SL(2,R) WZW model for states in arbitrary spectral flow sectors. We compute the leading order contribution to the expansion of the amplitudes in powers of the cross ratio of the four points on the worldsheet, both in the m- and x-basis, with at least one state in the spectral flow image of the highest weight discrete representation. We also perform certain consistency check on the winding conserving three point functions.