Correlation Functions of Winding Strings in AdS_3

TL;DR

This paper reviews spectral flowed operator amplitudes in string theory on AdS_3, deriving modified equations, analyzing three-point functions, and calculating winding conserving four-point functions across spectral sectors.

Contribution

It introduces modified Knizhnik-Zamolodchikov and null vector equations for spectral flowed operators and details the calculation of four-point functions in various spectral sectors.

Findings

Derived modified KZ and null vector equations for spectral flow

Analyzed three-point functions involving spectral flowed operators

Calculated winding conserving four-point functions in spectral sectors

Abstract

We review certain results for amplitudes of spectral flowed operators in string theory on AdS_3. We present the modified Knizhnik-Zamolodchikov and null vector equations to be satisfied by correlators including w=1 operators. We then discuss the three point function of two w=1 and one w=0 operators in the x-basis, and perform a consistency check on the definition of the w=1 operator. We finally exhibit the steps in the calculation of the winding conserving four point functions for operators in arbitrary spectral flowed sectors, both in the m- and x-basis, under the only assumption that at least one of the operators is in the spectral flowed image of the highest weight discrete representation.