Higher spins on AdS${}_3$ from the worldsheet

Abstract

It was recently shown that the CFT dual of string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times T^4$, the symmetric orbifold of $T^4$, contains a closed higher spin subsector. Via holography, this makes precise the sense in which tensionless string theory on this background contains a Vasiliev higher spin theory. In this paper we study this phenomenon directly from the worldsheet. Using the WZW description of the background with pure NS-NS flux, we identify the states that make up the leading Regge trajectory and show that they fit into the even spin $\mathcal{N}=4$ Vasiliev higher spin theory. We also show that these higher spin states do not become massless, except for the somewhat singular case of level $k=1$ where the theory contains a stringy tower of massless higher spin fields coming from the long string sector.

arXiv comment29+8 pages, 3 figures

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