The Worldsheet Dual of the Symmetric Product CFT

Monday, 3 December, 2018

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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.


Lorenz Eberhardt
Matthias R. Gaberdiel
Rajesh Gopakumar