A superspace approach to AdS$_3$ string theory

TL;DR

This paper develops a superspace framework for AdS3 string theory, constructing a free-field realization of the supersymmetric SL(2,R) WZW model, and computes correlation functions that suggest a new dual CFT description.

Contribution

It introduces a superspace approach and a free-field realization for AdS3 superstring theory, enabling exact correlation function calculations without picture-changing operators.

Findings

Exact tree-level correlation functions of long strings computed.

Proposal for a novel boundary CFT dual for heterotic superstrings in AdS3.

Demonstrates preservation of worldsheet supersymmetry in the free-field realization.

Abstract

We carefully examine the Polyakov path integral for strings on $\text{AdS}_3$ in superspace, both for type II and heterotic superstrings. We construct a free-field realization of the supersymmetric $\text{SL}(2,\mathbb{R})$ WZW model which manifestly preserves worldsheet supersymmetry and use this free-field realization to construct spectrally-flowed vertex operators describing the emission of long strings in the bulk. By working directly with the moduli space of super Riemann surfaces, we exactly compute tree-level correlation functions of long strings in the `near-boundary' limit without resorting to the standard picture-changing-operator (PCO) procedure. Finally, we argue how these correlators schematically reproduce correlation functions of the conjectured boundary CFTs, and as a result provide a novel proposal for the CFT dual for heterotic superstrings in $\text{AdS}_3$.