The worldsheet dual of the symmetric product CFT

Abstract

Superstring theory on {mathrm{AdS}}_3 times {S}^3times {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 SymN left({mathbb{T}}^4right) . To define the worldsheet theory at k = 1, we employ the hybrid formalism in which the AdS3 × S3 part is described by the mathfrak{p}mathfrak{s}mathfrak{u}{left(1,1Big|2right)}_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.