Winding modes and the reflection symmetry in AdS$_3$

TL;DR

This paper analyzes the SL(2,R)-WZNW model in AdS3, focusing on winding modes, reflection symmetry, and explicit computation of the two-point function contact term in spectral flow sectors.

Contribution

It provides an explicit form of the contact term for the two-point function in the spectral flowed sector, extending previous integral expressions.

Findings

Derived the contact term for the two-point function in spectral flow sectors.

Established the reflection symmetry for the spectral flowed sector.

Enhanced the integral expression for singly flowed vertices to reproduce the contact term.

Abstract

We compute the contact term of the two-point function for the SL($2,\mathbb R$)-WZNW model in the winding sector. After reviewing some generalities of the model and its Euclidean counterpart, we discuss the reflection symmetry for the spectral flowed sector. We define the corresponding intertwining operator and use it to find the explicit form of the contact term of the propagator for a vertex carrying an arbitrary amount of spectral flow. Finally, we enhance the already known integral expression of a singly flowed vertex in order to reproduce such contact term directly in the space-time picture.