The worldsheet dual of the symmetric product CFT

Abstract

Abstract Superstring theory on AdS 3 × S 3 × T 4 $$ {\mathrm{AdS}}_3 \times {S}^3\times {\mathbb{T}}^4 $$ 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 Sym N T 4 $$ \left({\mathbb{T}}^4\right) $$ . To define the worldsheet theory at k = 1, we employ the hybrid formalism in which the AdS3 × S3 part is described by the p s u 1 , 1 | 2 1 $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}{\left(1,1\Big|2\right)}_1 $$ WZW model (which is well defined). Unlike the case for k ≥ 2, it turns out that the string spectrum at k = 1 does 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.

Keywords

• AdS-CFT Correspondence
• Conformal Field Models in String Theory
• Long strings
• Superstrings and Heterotic Strings