On the Liouville three-point function

Abstract

The recently proposed expression for the general three point function of exponential fields in quantum Liouville theory on the sphere is considered. By exploiting locality or crossing symmetry in the case of those four-point functions, which may be expressed in terms of hypergeometric functions, a set of functional equations is found for the general three point function. It is shown that the expression proposed by the Zamolodchikovs solves these functional equations and that under certain assumptions the solution is unique.

8 Pages, LATEX

References in corpus (3)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Two and three-point functions in Liouville theory
• Continous Spins in 2D Gravity: Chiral Vertex Operators and Local Fields

Cited by in corpus (173)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Liouville theory revisited
• Liouville Field Theory -- A decade after the revolution
• Analytic Continuation of Liouville Theory
• Solving the Schwarzian via the Conformal Bootstrap
• On structure constants and fusion rules in the $SL(2,\BC)/SU(2)$ WZNW model
• Liouville field theory on a pseudosphere
• Branes, Rings and Matrix Models in Minimal (Super)string Theory
• Bootstrapping the superconformal index with surface defects
• Rolling Tachyons from Liouville theory
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• Correlation functions in conformal Toda field theory I
• Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Correlation functions in conformal Toda field theory II
• Exact vs. Semiclassical Target Space of the Minimal String
• Super Liouville Theory with Boundary
• Modular Bootstrap for Boundary N=2 Liouville Theory
• Liouville theory with a central charge less than one
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Structure Constants in the $N=1$ Super-Liouville Field Theory
• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Notes on AdS_3
• Higher Equations of Motion in Liouville Field Theory
• Bulk-Boundary Propagator in Liouville Theory on a Disc
• Exact One-Point Function of N=1 super-Liouville Theory with Boundary
• H^+_3 WZNW model from Liouville field theory
• The WZNW model on PSU(1,1|2)
• On three-point connectivity in two-dimensional percolation
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• The Mini-Superspace Limit of the SL(2,C)/SU(2)-WZNW Model
• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• Lectures on Branes in Curved Backgrounds
• On the Three-point Function in Minimal Liouville Gravity
• D-branes in N=2 Liouville and its mirror
• The Virasoro Minimal String
• Minimal String Theory
• Bulk correlation functions in 2D quantum gravity
• Hidden Grassmann structure in the XXZ model V: sine-Gordon model
• Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator
• Boundary Liouville Theory and 2D Quantum Gravity
• One-Point Functions of N=2 Super-Liouville Theory with Boundary
• Non-compact String Backgrounds and Non-rational CFT
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• Bilinear equations on Painleve tau functions from CFT
• Geometrical four-point functions in the two-dimensional critical $Q$-state Potts model: The interchiral conformal bootstrap
• Bootstrap in Supersymmetric Liouville Field Theory. I. NS Sector
• Annulus Amplitudes and ZZ Branes in Minimal String Theory
• Branes in the GL(1|1) WZNW-Model
• Dynamical actions and q-representation theory for double-scaled SYK
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Correlation functions in loop models
• Notes on Liouville Theory at c<=1
• Gauge Theory Wilson Loops and Conformal Toda Field Theory
• Three-point functions in AdS${}_3$/CFT${}_2$ holography
• Holomorphic blocks and the 5d AGT correspondence
• Intersecting Surface Defects and Two-Dimensional CFT
• Non-Rational 2D Quantum Gravity: I. World Sheet CFT
• ZZ-Branes of N=2 Super-Liouville Theory
• Non-Perturbative Topological Strings And Conformal Blocks
• Bootstrapping 2D CFTs in the Semiclassical Limit
• On Minisuperspace Models of S-branes
• Selberg Integral and SU(N) AGT Conjecture
• N=4 Superconformal Bootstrap of the K3 CFT
• N=2 Liouville Theory with Boundary
• D-branes and BCFT in Hpp-wave backgrounds
• Boundary Ground Ring in 2D String Theory
• On the timelike Liouville three-point function
• On AGT description of N=2 SCFT with N_f=4
• Quantum Gravity from Timelike Liouville theory
• From Spacetime to Worldsheet: Four point correlators
• D-branes in Singular Calabi-Yau n-fold and N=2 Liouville Theory
• Semiclassical and quantum Liouville theory on the sphere
• Spacelike boundaries from the c=1 Matrix Model
• The Stoyanovsky-Ribault-Teschner Map and String Scattering Amplitudes
• Liouville Theory on the Pseudosphere: Bulk-Boundary Structure Constant
• A brief review of the 2d/4d correspondences
• Standard and geometric approaches to quantum Liouville theory on the pseudosphere
• Duality in N=2 Super-Liouville Theory
• Matrix integrals $\&$ finite holography
• The DOZZ Formula from the Path Integral
• Long String Scattering in c = 1 String Theory
• Defects and Permutation branes in the Liouville field theory
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• Liouville Quantum Gravity
• Liouville theory without an action
• Riemann-Hilbert treatment of Liouville theory on the torus
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• Lecture notes on Liouville theory and the DOZZ formula
• Minimal Superstrings and Loop Gas Models
• The complex Liouville string: the matrix integral
• Duality in Quantum Liouville Theory
• Accessory parameters for Liouville theory on the torus
• The tetrahedron graph in Liouville theory on the pseudosphere
• Liouville Field Theory on an Unoriented Surface
• Polyakov's String: Twenty Five Years After
• The complex Liouville string: the worldsheet
• Liouville field theory with heavy charges. I. The pseudosphere
• Boundary Action of N=2 Super-Liouville Theory
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Branes in the OSP(1|2) WZNW model
• Integrability of Conformal Loop Ensemble: Imaginary DOZZ Formula and Beyond
• Integrability of Liouville theory: proof of the DOZZ Formula
• Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT
• Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
• Liouville Quantum Gravity and KPZ
• On the construction of the correlation numbers in Minimal Liouville Gravity
• Boundary Ground Ring in Minimal String Theory
• Super-Liouville - Double Liouville correspondence
• FZZ Algebra
• Matrix Models and 2D String Theory
• Quantum Liouville theory on the pseudosphere with heavy charges
• Energy Quantisation in Bulk Bouncing Tachyon
• FZZ Scattering
• The Two-exponential Liouville Theory and the Uniqueness of the Three-point Function
• Non-critical strings at high energy
• Tadpole Cancellation in Unoriented Liouville Theory
• The non-rational limit of D-series minimal models
• Expansions for semiclassical conformal blocks
• A Worldsheet Description of Instant Folded Strings
• Constructive Liouville Conformal Field Theory
• Critical loop models are exactly solvable
• Some remarks on D-branes and defects in Liouville and Toda field theories
• On classical and semiclassical properties of the Liouville theory with defects
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• Semiclassical limit of the FZZT Liouville theory
• Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
• Notes on D-branes and dualities in (p,q) minimal superstring theory
• Hyperbolic deformation of the strip-equation and the accessory parameters for the torus
• The complex Liouville string: the gravitational path integral
• Refined Cigar and Omega-deformed Conifold
• Semi-Classical Mechanics in Phase Space: The Quantum Target of Minimal Strings
• Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• Non-Compact Geometries in 2D Euclidean Quantum Gravity
• Conformal Bootstrap in dS/CFT and Topological Quantum Gravity
• Fusion asymptotics for Liouville correlation functions
• Critical Non-Abelian Vortex and Holography for Little String Theory
• The two-sphere partition function in two-dimensional quantum gravity at fixed area
• Liouville Conformal Field Theory on even-dimensional spheres
• The two-sphere partition function in two-dimensional quantum gravity
• Negative Screenings in Liouville Theory
• Probabilistic conformal blocks for Liouville CFT on the torus
• On the Virasoro fusion kernel at $c=25$
• Riemann-Hilbert treatment of Liouville theory on the torus: The general case
• Duality Constraints on String Theory: Instantons and spectral networks
• Crossing invariant correlation functions at $c=1$ from isomonodromic $\tau$ functions
• Semiclassical and quantum Liouville theory
• Generalized Toda Theory from Six Dimensions and the Conifold
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• On Krichever tau-function and Verlinde formula
• Modular bootstrap agrees with path integral in the large moduli limit
• Applications of Random Graphs to 2D Quantum Gravity
• Dual Frobenius manifolds of minimal gravity on disk
• Liouville Theory, AdS${}_2$ String, and Three-Point Functions
• On the tau function of the hypergeometric equation
• Notes on the SL(2,R) CFT
• Schwinger-Dyson approach to Liouville Field Theory
• Non invariant zeta-function regularization in quantum Liouville theory
• Logarithmic operators in $c=0$ bulk CFTs
• Boundary timelike Liouville theory: bulk 1-point & boundary 2-point functions
• Non-rational su(2) cosets and Liouville field theory
• On the analytical continuation of lattice Liouville theory
• Wronskians, dualities and FZZT-Cardy branes
• On the conformal bootstrap for SL(2,R)-WZNW models
• Strings and D-branes in holographic backgrounds
• Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance
• A Bäcklund transformation for elliptic four-point conformal blocks
• Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model
• Remarks on A_2 Toda Field Theory
• The semiclassical gravitational path integral and random matrices
• Highest-weight vectors and three-point functions in GKO coset decomposition
• Irreducible Virasoro representations in Liouville conformal field theory