Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A superspace approach to AdS$_3$ string theory

Bob Knighton, Nathan McStay, Vit Sriprachyakul

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 $\text{AdS}_3$.

A superspace approach to AdS$_3$ string theory

Abstract

We carefully examine the Polyakov path integral for strings on in superspace, both for type II and heterotic superstrings. We construct a free-field realization of the supersymmetric 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 .
Paper Structure (73 sections, 336 equations, 1 figure)

This paper contains 73 sections, 336 equations, 1 figure.

Table of Contents

  1. Introduction
  2. A manifestly supersymmetric approach:
  3. Computing near-boundary correlators:
  4. Note:
  5. The worldsheet SCFT
  6. The AdS3 sigma model
  7. Decoupling the fields:
  8. The reduced action:
  9. Quantization
  10. Relation to the $\text{SL}(2,\mathbb{R})$ WZW model:
  11. Representations and spectral flow
  12. Spectral flow:
  13. The $x$-basis:
  14. The Ramond sector
  15. The standard description:
  16. ...and 58 more sections

Figures (1)

  • Figure 1: A worldsheet instanton can move arbitrarily close to the boundary of $\text{AdS}_3$ at a finite cost of energy.