H^+_3 WZNW model from Liouville field theory

Abstract

There exists an intriguing relation between genus zero correlation functions in the H^+_3 WZNW model and in Liouville field theory. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program.

33 pages, no figure, minor changes, several equations corrected

References in corpus (25)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Two and three-point functions in Liouville theory
• On the Liouville three-point function
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
• On structure constants and fusion rules in the $SL(2,\BC)/SU(2)$ WZNW model
• Liouville field theory on a pseudosphere
• Remarks on Liouville theory with boundary
• H(3)+ correlators from Liouville theory
• Correlators in AdS_3 string theory
• Branes in the Euclidean AdS_3
• Comments On String Theory
• The Mini-Superspace Limit of the SL(2,C)/SU(2)-WZNW Model
• Non-compact String Backgrounds and Non-rational CFT
• Non-Compact WZW Conformal Field Theories
• A relation between the Knizhnik--Zamolodchikov and Belavin--Polyakov--Zamolodchikov systems of partial differential equations
• Branes in the GL(1|1) WZNW-Model
• Comments on String Theory on $Ad{S}_3$
• Free Field Appoach to String Theory on AdS_3
• The Stoyanovsky-Ribault-Teschner Map and String Scattering Amplitudes
• Separation of variables for quantum integrable systems on elliptic curves
• Solution of the H3+ model on a disc
• The String Theory on AdS_3 as a Marginal Deformation of a Linear Dilaton Background
• New boundary conditions for the c=-2 ghost system
• Notes On The S-Matrix Of Bosonic And Topological Non-Critical Strings
• Separation of variables for Gaudin-Calogero systems

Cited by in corpus (54)

• Affine SL(2) conformal blocks from 4d gauge theories
• The Schwarzian Theory - A Wilson Line Perspective
• Instanton counting with a surface operator and the chain-saw quiver
• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• $T\bar{T}$-deformations, AdS/CFT and correlation functions
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Surface Operators and Separation of Variables
• String correlators on ${\text{AdS}}_3$: Three-point functions
• Modular bootstrap in Liouville field theory
• Branes in the GL(1|1) WZNW-Model
• The FZZ-Duality Conjecture - A Proof
• String correlators on ${\text{AdS}}_3$: Analytic structure and dual CFT
• Structure constants of the OSP(1|2) WZNW model
• $T\bar{T}$ type deformation in the presence of a boundary
• On AGT description of N=2 SCFT with N_f=4
• Rectangular W-algebras, extended higher spin gravity and dual coset CFTs
• On the fusion matrix of the N=1 Neveu-Schwarz blocks
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• Rectangular W-(super)algebras and their representations
• Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3\times {\mathbf{T}}^4$
• Violating the string winding number maximally in Anti-de Sitter space
• Supergroup - extended super Liouville correspondence
• Boundary action of the H3+ model
• On sl3 Knizhnik-Zamolodchikov equations and W3 null-vector equations
• Intersecting Defects and Supergroup Gauge Theory
• Correspondences among CFTs with different W-algebra symmetry
• Branes in the OSP(1|2) WZNW model
• The FZZ duality with boundary
• Correspondences between WZNW models and CFTs with W-algebra symmetry
• On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• $T\bar{T}$ deformation of classical Liouville field theory
• One-loop amplitudes of winding strings in AdS${}_3$ and the Coulomb gas approach
• Topological expansion and boundary conditions
• A family of solvable non-rational conformal field theories
• A note on the spectral flow operator
• String correlators in AdS${}_3$ from FZZ duality
• Current-current deformations, conformal integrals and correlation functions
• Higher rank FZZ-dualities
• Topological String on OSP(1|2)/U(1)
• Yangian Superalgebras in Conformal Field Theory
• Stringy horizons and generalized FZZ duality in perturbation theory
• Disk one-point function for non-rational conformal theories
• String correlators on ${\text{AdS}}_3$: Four-point functions
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• Kappa symmetric OSp(2|2) WZNW model
• On string theory on AdS${}_3\times M_7$ in the tensionless limit
• Notes on the SL(2,R) CFT
• $N=1$ super Virasoro tensor categories
• Non-rational su(2) cosets and Liouville field theory
• Conformal field theories from deformations of theories with $W_n$ symmetry
• Correlator correspondences for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality