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.

29+8 pages, 3 figures

References in corpus (6)

• Higher Spins & Strings
• BPS spectrum on AdS${}_3\times$S${}^3\times$S${}^3\times$S${}^1$
• Tensionless Superstrings: View from the Worldsheet
• The symmetry of large N=4 holography
• Spinning strings and minimal surfaces in $Ad{S}_3$ with mixed 3-form fluxes
• Counting Giant Gravitons in AdS_3

Cited by in corpus (39)

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• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• Strings on NS-NS Backgrounds as Integrable Deformations
• Superstrings on AdS3 at k=1
• A holographic dual for string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Inhomogeneous Tensionless Superstrings
• Integrable S matrix, mirror TBA and spectrum for the stringy ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$ WZW model
• Higher genus correlators for tensionless ${\mathrm{AdS}}_3$ strings
• Three-point functions in AdS${}_3$/CFT${}_2$ holography
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• The supersymmetric affine Yangian
• Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian
• Stringy $\mathcal{N}=(2,2)$ holography for AdS${}_3$
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Higher spin algebras and large $\mathcal{N}=4$ holography
• Long strings and chiral primaries in the hybrid formalism
• The plane-wave spectrum from the worldsheet
• DDF operators in the Hybrid Formalism
• Twistor Coverings and Feynman Diagrams
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• A localising AdS${}_3$ sigma model
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• A note on the spectral flow operator
• Stringy CFT Duals with $\mathcal{N}=(2,2)$ Supersymmetry
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model
• The Higher Spin Rectangle
• The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten spin-chain $\sigma$-model
• Asymptotically Free AdS3/CFT2
• Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography
• On tensionless string field theory in AdS${}_3$
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography
• On string theory on AdS${}_3\times M_7$ in the tensionless limit
• The physical states of the Hybrid Formalism
• D-Branes in ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Non-supersymmetric strings on AdS${}_3$: a world-sheet perspective
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality