Free field world-sheet correlators for ${\mathrm{AdS}}_3$

Abstract

We employ the free field realisation of the $\mathfrak{psu}(1,1|2{)}_1$ world-sheet theory to constrain the correlators of string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathbb{T}}^4$ with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary ${\mathrm{S}}^2$ by the (genus zero) world-sheet -- this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable `incidence relation' obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.

arXiv comment42 pages

References in corpus (35)

• Perturbative Gauge Theory As A String Theory In Twistor Space
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• The Worldsheet Dual of the Symmetric Product CFT
• On the Tree-Level S-Matrix of Yang-Mills Theory
• Correlation functions for M^N/S_N orbifolds
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• N=4 Topological Strings
• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• Phases of Quantum Gravity in AdS3 and Linear Dilaton Backgrounds
• Diagrams for Symmetric Product Orbifolds
• Superstrings on AdS3 at k=1
• The WZNW model on PSU(1,1|2)
• The Mini-Superspace Limit of the SL(2,C)/SU(2)-WZNW Model
• Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theory
• The su(2)_{-1/2} WZW model and the beta-gamma system
• Crossing Symmetry in the $H_3^{+}$ WZNW model
• Correlators of the symmetric product orbifold
• Strings on ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$
• The logarithmic triplet theory with boundary
• Fusion in Fractional Level sl^(2)-Theories with k=-1/2
• Modular transformation and boundary states in logarithmic conformal field theory
• Axiomatic Conformal Field Theory
• Boundary Spectra in Superspace Sigma-Models
• Comments on the $S_N$ orbifold CFT in the large $N$-limit
• Superspace conformal field theory
• String States on AdS_3 x S^3 from the Supergroup
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
• Fusion rules and four-point functions in the AdS3 WZNW model
• On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation
• Minisuperspace limit of the AdS3 WZNW model
• Twisted String Theory in Anti-de Sitter Space

Cited by in corpus (37)

• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Summing over Geometries in String Theory
• A Derivation of AdS/CFT for Vector Models
• String correlators on ${\text{AdS}}_3$: Three-point functions
• Tree-level amplitudes from the pure spinor superstring
• The String Dual to Free $\mathcal{N}=4$ Super Yang-Mills
• Higher genus correlators for tensionless ${\mathrm{AdS}}_3$ strings
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• String correlators on ${\text{AdS}}_3$: Analytic structure and dual CFT
• Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold
• BPS Correlators for ${\text{AdS}}_3/{\text{CFT}}_2$
• Perturbing the symmetric orbifold from the worldsheet
• The free field realisation of the BVW string
• Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3\times {\mathbf{T}}^4$
• Stress-energy tensor correlators from the world-sheet
• DDF operators in the Hybrid Formalism
• Twistor Coverings and Feynman Diagrams
• Superstrings in Thermal Anti-de Sitter Space
• A localising AdS${}_3$ sigma model
• Dynamical evolution in the D1D5 CFT
• A duality in string theory on AdS${}_3$
• Quantum Entanglement on Black Hole Horizons in String Theory and Holography
• String correlators in AdS${}_3$ from FZZ duality
• The Dual of a Tidal Force in the D1D5 CFT
• AdS from CFT for scalar QED
• Classical geometry from the tensionless string
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Free BMN Correlators With More Stringy Modes
• The physical states of the Hybrid Formalism
• Space-time symmetry from the world-sheet
• String theory in twistor space and minimal tension holography
• D-Branes in ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$
• Worldsheet Free Fields, Higher Spin Symmetry and Free $\mathcal{N}=4$ Super Yang-Mills
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Illuminating entanglement shadows of BTZ black holes by a generalized entanglement measure
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality