# The Worldsheet Dual of the Symmetric Product CFT

## TL;DR

This paper establishes a duality between superstring theory on a specific AdS3 background at minimal flux and a symmetric product orbifold CFT, providing a tractable worldsheet description of a tensionless string limit.

## Contribution

It constructs a worldsheet theory at minimal flux using the hybrid formalism and shows it matches the symmetric orbifold CFT, including spectrum and fusion rules.

## Key findings

- String spectrum at k=1 lacks long string continuum.
- Worldsheet fusion rules match symmetric orbifold.
- Provides a worldsheet description of a tensionless limit.

## Abstract

Superstring theory on ${\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with the smallest amount of NS-NS flux (`$k=1$') is shown to be dual to the spacetime CFT given by the large $N$ limit of the free symmetric product orbifold $\mathrm{Sym}^N(\mathbb{T}^4)$. To define the worldsheet theory at $k=1$, we employ the hybrid formalism in which the ${\rm AdS}_3\times {\rm S}^3$ part is described by the $\mathfrak{psu}(1,1|2)_1$ WZW model (which is well defined). Unlike the case for $k\geq2$, it turns out that the string spectrum at $k=1$ does {\it not} exhibit the long string continuum, and perfectly matches with the large $N$ limit of the symmetric product. We also demonstrate that the fusion rules of the symmetric orbifold are reproduced from the worldsheet perspective. Our proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory, for which the dual CFT is also explicitly known.