The $AdS_3 \times S^1$ Chiral Ring

TL;DR

This paper analyzes supersymmetric string backgrounds with $AdS_3 imes S^1 imes Y$ geometry, classifies chiral primaries, and computes their structure constants, revealing a universal form tied to the boundary theory's topology.

Contribution

It classifies worldsheet vertex operators for space-time chiral primaries and computes their structure constants, showing a universal dependence on the boundary theory's topological data.

Findings

Chiral primary operators are classified on the worldsheet.

Space-time chiral ring structure constants are computed.

Structure constants depend only on the topological data of the boundary theory.

Abstract

We study $AdS_3 \times S^1 \times Y$ supersymmetric string theory backgrounds with Neveu-Schwarz-Neveu-Schwarz flux that are dual to ${\cal N}=2$ superconformal theories on the boundary. We classify all worldsheet vertex operators that correspond to space-time chiral primaries. We compute space-time chiral ring structure constants for operators in the zero spectral flow sector using the operator product expansion in the worldsheet theory. We find that the structure constants take a universal form that depends only on the topological data of the ${\cal N}=2$ superconformal theory on $Y$.