Spectral flow and localisation in $\text{AdS}_3$ string theory

TL;DR

This paper analyzes string theory in AdS3, deriving vertex operators, relating correlation functions to covering maps, and exploring localization properties, especially for the case of IIB string theory with minimal flux.

Contribution

It provides a path integral derivation of spectral flow and localization in AdS3 string theory, connecting correlation functions to covering maps and dual theories.

Findings

Correlation functions relate to covering maps from the worldsheet to the boundary.

Spectral flow can be interpreted as a background gauge field introducing localization.

The k=1 case of IIB string theory exhibits a sharp relationship between correlation functions and covering maps.

Abstract

We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on $\text{AdS}_3\times\text{S}^3\times\mathbb{T}^4$ with $k=1$ units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the $k=1$ theory and twistor theory.