A holographic dual for string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$

Abstract

The CFT dual of string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ is conjectured to be the symmetric orbifold of the ${\mathcal{S}}_{\kappa }$ theory, provided that one of the two $Q_5^{\pm }$ quantum numbers is a multiple of the other. We determine the BPS spectrum of the symmetric orbifold in detail, and show that it reproduces precisely the BPS spectrum that was recently calculated in supergravity. We also determine the BPS spectrum of the world-sheet theory that is formulated in terms of WZW models, and show that, apart from some gaps (which are reminiscent of those that appear in the corresponding ${\mathbb{T}}^4$ calculation), it also reproduces this BPS spectrum. In fact, the matching seems to work as well as for the familiar ${\mathbb{T}}^4$ case, and thus our results give strong support for this proposal.

41 pages, 2 figures

References in corpus (7)

• Higher Spins & Strings
• A non-renormalization theorem for chiral primary 3-point functions
• BPS spectrum on AdS${}_3\times$S${}^3\times$S${}^3\times$S${}^1$
• Protected string spectrum in AdS3/CFT2 from worldsheet integrability
• Higher spins on AdS${}_3$ from the worldsheet
• Counting Giant Gravitons in AdS_3
• An Index for 2D field theories with large N=4 superconformal symmetry

Cited by in corpus (62)

• The Worldsheet Dual of the Symmetric Product CFT
• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• Superstrings on AdS3 at k=1
• String theory on ${\text{AdS}}_3$ and the symmetric orbifold of Liouville theory
• Two dimensional $\mathcal{N}=(0,4)$ quivers dual to AdS${}_3$ solutions in massive IIA
• Partition functions of the tensionless string
• Strings on ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$
• Type II Solutions on AdS${}_3\times S^3\times S^3$ with Large Superconformal Symmetry
• 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
• Supersymmetric ${\mathrm{AdS}}_3$ supergravity backgrounds and holography
• Instanton R-matrix and W-symmetry
• Stringy $\mathcal{N}=(2,2)$ holography for AdS${}_3$
• Information transfer with a twist
• Yangian Symmetry of String Theory on $Ad{S}_3\times S^3\times S^3\times S^1$ with Mixed 3-form Flux
• Higher spin algebras and large $\mathcal{N}=4$ holography
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Kaluza-Klein spectrometry for $\mathrm{Ad}{\mathrm{S}}_3$ vacua
• Long strings and chiral primaries in the hybrid formalism
• The plane-wave spectrum from the worldsheet
• Triality and the consistent reductions on ${\mathrm{AdS}}_3\times S^3$
• $\mathcal{N}=(1,1)$ supersymmetric AdS${}_3$ in 10 dimensions
• Superstrings in Thermal Anti-de Sitter Space
• On generalised D1-D5 near horizons and their spectra
• One-loop quantization of rigid spinning strings in $Ad{S}_3\times S^3\times T^4$ with mixed flux
• A localising AdS${}_3$ sigma model
• The $\mathcal{N}=4$ Coset Model and the Higher Spin Algebra
• Wrapped Fivebranes Redux
• The $\mathcal{N}=4$ Higher Spin Algebra for Generic $\mu$ Parameter
• Quantum Corrections to Central Charges and Supersymmetric Casimir Energy in AdS${}_3$/CFT${}_2$
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• Boost generator in AdS_3 integrable superstrings for general braiding
• String correlators in AdS${}_3$ from FZZ duality
• Fortuity and Supergravity
• A study of integrable form factors in massless relativistic AdS_3
• On the abundance of supersymmetric strings in $Ad{S}_3\times S^3\times S^3\times S^1$ describing BPS line operators
• Charting the Conformal Manifold of Holographic CFT${}_2$'s
• Symmetries of the refined D1/D5 BPS spectrum
• Mellin amplitudes for $Ad{S}_3\times S^3$
• On N-spike strings in conformal gauge with NS-NS fluxes
• Stringy CFT Duals with $\mathcal{N}=(2,2)$ Supersymmetry
• A Supersymmetric Enhancement of $\mathcal{N}=1$ Holographic Minimal Model
• The plane-wave limit of ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$
• Adding Complex Fermions to the Grassmannian-like Coset Model
• On multi-spin classical strings with NS-NS flux
• Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• Higher Spin Currents with Manifest $SO(4)$ Symmetry in the Large $\mathcal{N}=4$ Holography
• Geometry of Massless Scattering in Integrable Superstring
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• $N$-spike string in $Ad{S}_3\times S^1$ with mixed flux
• The Grassmannian VOA
• Central charges, elliptic genera, and Bekenstein-Hawking entropy in $\mathcal{N}=(2,2)$ AdS${}_3$/CFT${}_2$
• Semiclassical quantization of the mixed-flux AdS${}_3$ giant magnon
• Non-supersymmetric strings on AdS${}_3$: a world-sheet perspective
• A New Supersymmetry Index for the D1-D5 CFT
• Winding modes and the reflection symmetry in AdS${}_3$
• The Resolved Elliptic Genus and the D1-D5 CFT
• New AdS${}_3$/CFT${}_2$ pairs in massive IIA with $(0,4)$ and $(4,4)$ supersymmetries
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• Neumann-Rosochatius system for rotating strings in $Ad{S}_3\times S^3\times S^3\times S^1$ with flux