Spectral flow and conformal blocks in $AdS_3$

TL;DR

This paper analyzes four-point functions in the $AdS_3$-WZNW model, revealing how conformal blocks relate to extremal-weight states and extending the analysis to spectral flow cases, providing explicit integral formulas.

Contribution

It introduces a method to derive conformal blocks from extremal-weight states and extends the analysis to spectral flow sectors in the $AdS_3$-WZNW model.

Findings

Conformal blocks can be obtained via an intertwining operator.

Factorized integral expressions for spectral flow correlators are derived.

Formulas are transformed back to the space-time picture.

Abstract

In this article we investigate the structure of the four-point functions of the $AdS_3$-WZNW model. We consider the integral expression for the unflowed four-point correlator involving at least one state in the discrete part of the spectrum derived by analytic continuation from the $H_3^+$-WZNW model and we show that the conformal blocks can be obtained from those with an extremal-weight state by means of an intertwining operator. We adapt the procedure for dealing with correlators with a single unit of spectral flow charge and we get a factorized integral expression for the corresponding four-point function. We finally transform the formulas back to the space-time picture.