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The worldsheet dual of the symmetric product CFT

  • Lorenz EberhardtEmail author
  • Matthias R. Gaberdiel
  • Rajesh Gopakumar
Open Access
Regular Article - Theoretical Physics
  • 19 Downloads

Abstract

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

Notes

Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Institut für Theoretische Physik, ETH ZurichZürichSwitzerland
  2. 2.International Centre for Theoretical Sciences-TIFRBengaluru NorthIndia

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