The worldsheet dual of the symmetric product CFT

By Lorenz Eberhardt, M. Gaberdiel, Rajesh Gopakumar. Journal of High Energy Physics, 2018

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A bstractSuperstring theory on AdS3×S3×T4$$ {\mathrm{AdS}}_3 \times {S}^3\times {\mathbb{T}}^4 $$ 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 SymNT4$$ \left({\mathbb{T}}^4\right) $$. To define the worldsheet theory at k = 1, we employ the hybrid formalism in which the AdS3 × S3 part is described by the psu1,1|21$$ \mathfrak{p}\mathfrak{s}\mathfrak{u}{\left(1,1\Big|2\right)}_1 $$ 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.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a99e34618408adb36c7536972d51852937a8dd8f