Liouville theory revisited

Abstract

We try to develop a coherent picture on Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we need to develop further some of these approaches. This includes in particular a construction of general exponential field operators from a set of covariant chiral operators. The latter are shown to satisfy braid relations that allow one to prove the locality of the former.

78 pages, uses bourbaki.cls; some remarks in sec. 9 altered, minor corrs

Cited by in corpus (250)

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• Analytic Continuation of Liouville Theory
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Solving the Schwarzian via the Conformal Bootstrap
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Branes, Rings and Matrix Models in Minimal (Super)string Theory
• Power-law out of time order correlation functions in the SYK model
• A Matrix Model Dual of Type 0B String Theory in Two Dimensions
• Gauge Theory Loop Operators and Liouville Theory
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Rolling Tachyons from Liouville theory
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Classical and Quantum D-branes in 2D String Theory
• Phases of Quantum Gravity in AdS3 and Linear Dilaton Backgrounds
• Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory
• LSZ in LST
• A lecture on the Liouville vertex operators
• Irregular singularities in Liouville theory
• H(3)+ correlators from Liouville theory
• The Schwarzian Theory - Origins
• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
• Conformal Bootstrap, Universality and Gravitational Scattering
• Irregular Liouville correlators and connection formulae for Heun functions
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• Universal Dynamics of Heavy Operators in CFT${}_2$
• M5-branes, toric diagrams and gauge theory duality
• The Tachyon at the End of the Universe
• String theory on ${\text{AdS}}_3$ and the symmetric orbifold of Liouville theory
• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Higher Equations of Motion in Liouville Field Theory
• Branes in the Euclidean AdS_3
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• On CFT and Quantum Chaos
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• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• On the spectrum of the Sinh-Gordon model in finite volume
• The su(2)_{-1/2} WZW model and the beta-gamma system
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Solving 3d Gravity with Virasoro TQFT
• Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
• Lectures on Branes in Curved Backgrounds
• D-branes in N=2 Liouville and its mirror
• The Virasoro Minimal String
• Three-point functions in c <= 1 Liouville theory and conformal loop ensembles
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• On the relation between quantum Liouville theory and the quantized Teichm"uller spaces
• Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• Classical geometry from the quantum Liouville theory
• The nuts and bolts of the BMS Bootstrap
• Painlevé VI connection problem and monodromy of c=1 conformal blocks
• Modular bootstrap in Liouville field theory
• Chiral Liouville Gravity
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Dynamical actions and q-representation theory for double-scaled SYK
• Completeness of Bethe Ansatz by Sklyanin SOV for Cyclic Representations of Integrable Quantum Models
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• Rolling Tachyon Boundary State, Conserved Charges and Two Dimensional String Theory
• Notes on Liouville Theory at c<=1
• The FZZ-Duality Conjecture - A Proof
• De Sitter Gravity and Liouville Theory
• String Scattering from Decaying Branes
• Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ
• Recursion representation of the Neveu-Schwarz superconformal block
• A slow review of the AGT correspondence
• String correlators on ${\text{AdS}}_3$: Analytic structure and dual CFT
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Monodromy of solutions of the Knizhnik-Zamolodchikov equation: SL(2,C)/SU(2) WZNW model
• Non-Perturbative Topological Strings And Conformal Blocks
• Notes on Matrix Models
• N=1 SUSY Conformal Block Recursive Relations
• The Large N Harmonic Oscillator as a String Theory
• Bootstrapping 2D CFTs in the Semiclassical Limit
• From 6D SCFTs to Dynamic GLSMs
• SYK model with quadratic perturbations: the route to a non-Fermi-liquid
• Selberg Integral and SU(N) AGT Conjecture
• Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
• Two-Dimensional Unoriented Strings And Matrix Models
• On boundary correlators in Liouville theory on AdS${}_2$
• The Holographic Ward identity: Examples from 2+1 gravity
• Structure constants of the OSP(1|2) WZNW model
• Boundary Liouville theory at c=1
• N=2 Liouville Theory with Boundary
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Liouville Conformal Field Theories in Higher Dimensions
• Vertices from replica in a random matrix theory
• Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
• On Superstring Disk Amplitudes in a Rolling Tachyon Background
• 't Hooft Operators in Gauge Theory from Toda CFT
• Boundary RG Flow Associated with the AKNS Soliton Hierarchy
• Twenty-five years of two-dimensional rational conformal field theory
• Quantum Liouville theory in the background field formalism I. Compact Riemann surfaces
• On AGT description of N=2 SCFT with N_f=4
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• From Spacetime to Worldsheet: Four point correlators
• Quantum Gravity from Timelike Liouville theory
• Flag manifold sigma models: spin chains and integrable theories
• The Stoyanovsky-Ribault-Teschner Map and String Scattering Amplitudes
• The universal Racah-Wigner symbol for Uq(osp(1|2))
• Classical Liouville action on the sphere with three hyperbolic singularities
• Semiclassical and quantum Liouville theory on the sphere
• $q$-Virasoro modular double and 3d partition functions
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• Modeling Quantum Gravity Effects in Inflation
• 3d mirror symmetry as a canonical transformation
• Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits
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• Stringy ER=EPR
• Bootstrapping closed string field theory
• Local logarithmic correlators as limits of Coulomb gas integrals
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• Standard and geometric approaches to quantum Liouville theory on the pseudosphere
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• The DOZZ Formula from the Path Integral
• Long String Scattering in c = 1 String Theory
• Discrete evolution for the zero-modes of the Quantum Liouville Model
• Liouville Perturbation Theory
• Strong coupling expansion for general relativity
• Defects and Permutation branes in the Liouville field theory
• AdS/BCFT from Conformal Bootstrap: Construction of Gravity with Branes and Particles
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• A note on entanglement entropy for topological interfaces in RCFTs
• Liouville Quantum Gravity
• On The Problem of Particle Production in c=1 Matrix Model
• Braiding properties of the N=1 super-conformal blocks (Ramond sector)
• Sinh-Gordon Boundary TBA and Boundary Liouville Reflection Amplitude
• Heavy-Heavy-Light-Light correlators in Liouville theory
• Self-dual Continuous Series of Representations for U_q(sl(2)) and U_q(osp(1|2))
• dS${}_2$ Supergravity
• Riemann-Hilbert treatment of Liouville theory on the torus
• Yangian associated with 2D $\mathcal{N}=1$ SCFT
• Liouville theory without an action
• Scattered Results in 2D String Theory
• Minimal Superstrings and Loop Gas Models
• The tetrahedron graph in Liouville theory on the pseudosphere
• Quantum Cosmology Near Two Dimensions
• Accessory parameters for Liouville theory on the torus
• Liouville Field Theory on an Unoriented Surface
• Classical limit of irregular blocks and Mathieu functions
• Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT
• A Note on Black Hole Entropy in Loop Quantum Gravity
• Liouville field theory and log-correlated Random Energy Models
• ADM reduction of Einstein action and black hole entropy
• c < 1 String from Two Dimensional Black Holes
• Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
• Remarks on free field realization of SL(2,R)/U(1) x U(1) WZNW model
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Quantum Liouville theory versus quantized Teichmüller spaces
• Operator Approach to Boundary Liouville Theory
• On the construction of the correlation numbers in Minimal Liouville Gravity
• Quantum line operators from Lax pairs
• Liouville field theory for gluon saturation in QCD at high energy
• Quantum exponentials for the modular double and applications in gravity models
• Semiclassical Gravity from Averaged Boundaries in two-dimensional BCFTs
• $\mathcal{N}=1$ Liouville SCFT in Four Dimensions
• Liouville's Imaginary Shadow
• Super-Liouville - Double Liouville correspondence
• Hartle-Hawking state and its factorization in 3d gravity
• FZZ Algebra
• Schwarzian functional integrals calculus
• Trinion Conformal Blocks from Topological strings
• FZZ Scattering
• Fermion Pairing and the Scalar Boson of the 2D Conformal Anomaly
• Boundary three-point function on AdS2 D-branes
• Energy Quantisation in Bulk Bouncing Tachyon
• Notes on D-branes in 2D Type 0 String Theory
• Quantum Liouville theory on the pseudosphere with heavy charges
• AFLT-type Selberg integrals
• Another derivation of the geometrical KPZ relations
• Toda theory in AdS${}_2$ and $\mathcal{W}{A}_n$-algebra structure of boundary correlators
• Liouville field theory with heavy charges. II. The conformal boundary case
• Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials
• The Kontsevich Connection on the Moduli Space of FZZT Liouville Branes
• Zamolodchikov relations and Liouville hierarchy in SL(2,R)_k WZNW model
• A family of solvable non-rational conformal field theories
• Some remarks on D-branes and defects in Liouville and Toda field theories
• A duality in string theory on AdS${}_3$
• Gauge Invariant Computable Quantities In Timelike Liouville Theory
• Mabuchi spectrum from the minisuperspace
• Torus classical conformal blocks
• Smoothness of correlation functions in Liouville Conformal Field Theory
• A parafermionic hypergeometric function and supersymmetric 6j-symbols
• 2D quantum gravity partition function on the fluctuating sphere
• Branes in JT (super)gravity from group theory
• On the solution of Liouville equation
• Long String Dynamics in Pure Gravity on AdS${}_3$
• Semiclassical limit of the FZZT Liouville theory
• BRST cohomology of timelike Liouville theory
• The Ground Ring of N=2 Minimal String Theory
• Symmetry-breaking boundary states for WZW models
• Semi-Classical Mechanics in Phase Space: The Quantum Target of Minimal Strings
• On the time-dependent description for the decay of unstable D-branes
• Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models
• Odd Dimensional Nonlocal Liouville Conformal Field Theories
• The Virasoro structure and the scattering matrix for Liouville conformal field theory
• Minisuperspace computation of the Mabuchi spectrum
• Crosscap states in N=2 Liouville theory
• Critical Non-Abelian Vortex and Holography for Little String Theory
• The two-sphere partition function in two-dimensional quantum gravity at fixed area
• Ward identities in the ${\mathfrak{sl}}_3$ Toda conformal field theory
• Topological Entanglement Entropy in Euclidean AdS3 via Surgery
• Physical Cosmological Constant in Asymptotically Background Free Quantum Gravity
• Liouville Conformal Field Theory on even-dimensional spheres
• On the S-matrix of Liouville theory
• Scale Symmetry in the Universe
• A Note on Z_2 Symmetries of the KZ Equation
• Singular Liouville fields and spiky strings in $\rr^{1,2}$ and $SL(2,\rr)$
• Non-renormalization for the Liouville wave function
• Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics
• A Causal Algebra for Liouville Exponentials
• The two-sphere partition function in two-dimensional quantum gravity
• Disk one-point function for non-rational conformal theories
• Joining-splitting interaction of non-critical string
• Riemann-Hilbert treatment of Liouville theory on the torus: The general case
• Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
• Gravitational action for a massive Majorana fermion in 2d quantum gravity
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• The Virasoro fusion kernel and Ruijsenaars' hypergeometric function
• Semiclassical and quantum Liouville theory
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• Crossing invariant correlation functions at $c=1$ from isomonodromic $\tau$ functions
• Semi-Classical Analysis of the String Theory Cigar
• Renormalization of lattice field theories with infinite-range wavelets
• Quantum Analytic Langlands Correspondence
• Conformal Dimensions On Causal Random Geometry
• The chiral SYK model in three-dimensional holography
• Quantum dilaton gravity as a linear dilaton conformal field theory
• A General Representation for the Green's Function of Second Order Nonlinear Differential Equations
• Liouville Theory, AdS${}_2$ String, and Three-Point Functions
• On a relation between Liouville field theory and a two component scalar field theory passing through the random walk
• Primordial fluctuations in extended Liouville theory
• Lattice String Field Theory: The linear dilaton in one dimension
• Quantisation of Gauged SL(2,R) WZNW Theories
• Four-point correlation modular bootstrap for OPE densities
• Baxterization of GL_q(2) and its application to the Liouville model and some other models on a lattice
• Comments on Quantum Aspects of Three-Dimensional de Sitter Gravity
• Asymptotic Symmetry and Classical holographic dual of $d{S}_3$ supergravity
• Non invariant zeta-function regularization in quantum Liouville theory
• Liouville soliton surfaces obtained using Darboux transformations
• Non-critical string, Liouville theory and geometric bootstrap hypothesis
• Probabilistic construction of non compactified imaginary Liouville field theory
• Studies on Polyakov and Nambu-Goto Random Surface Path Integrals on QCD (SU(infinity)): Interquark Potential and Phenomenological Scattering Amplitudes
• Quantum field theory with an interaction on the boundary
• The symmetric branes of the H4 WZW model
• Towards $W_3$ classical blocks with semi-degenerate operators