Liouville Field Theory -- A decade after the revolution

Abstract

We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. In part III, the Liouville theory on unoriented surfaces is reviewed. After introducing the crosscap state, we discuss the matrix model dual description and the tadpole cancellation condition. This review also includes some original material such as the derivation of the conjectured dual action for the N = 2 Liouville theory from other known dualities and the comparison of the Liouville crosscap state with the c = 0 unoriented matrix model. This is based on my master's thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2004.

264 pages, 31 figures, based on master's thesis defended 31/01/2004, v2,3,4,5,6,7: references added, typos corrected, abridged version published in IJMPA

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• On the Problems with Background Independence in String Theory
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• Continous Spins in 2D Gravity: Chiral Vertex Operators and Local Fields
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• Topological String on AdS_3 x N
• Rolling Tachyon with Electromagnetic Field in Linear Dilaton Background
• The Two-exponential Liouville Theory and the Uniqueness of the Three-point Function
• Classical and Quantum Branes in c=1 String Theory and Quantum Hall Effect
• 2d, N=2 and N=4 supergravity and the Liouville theory in superspace
• Nonsinglet Sector of $c=1$ Matrix Model and 2D Black Hole
• Topological Aspects of Quantum Gravity
• Strings, Black Holes and Conformal Field Theory
• Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory
• The Untruncated Marinari-Parisi Superstring
• The no-ghost theorem in curved backgrounds with a timelike u(1): NSR string
• Effective d=2 supersymmetric Lagrangians from d=1 supermatrix models
• Recent progress on Liouville Field Theory
• Using Functional Methods to Compute Quantum Effects in the Liouville Model
• Supersymmetric Field Theory from Supermatrix Models
• Zero Mode Problem of Liouville Field Theory
• Duality in Liouville Theory as a Reduced Symmetry
• c=1 String as a Topological Model
• On the Liouville coupling constants
• Factorization and Discrete States in C=1 Superliouville Theory
• On Quantum Black Holes

Cited by in corpus (227)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• The Pomeron and Gauge/String Duality
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Analytic Continuation of Liouville Theory
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• TFT construction of RCFT correlators III: Simple currents
• Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity
• Phases of Quantum Gravity in AdS3 and Linear Dilaton Backgrounds
• The Annular Report on Non-Critical String Theory
• Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory
• Critical Gaussian multiplicative chaos: Convergence of the derivative martingale
• H(3)+ correlators from Liouville theory
• TFT construction of RCFT correlators IV: Structure constants and correlation functions
• Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline
• Thermodynamics of Black Holes in Two (and Higher) Dimensions
• M5-branes, toric diagrams and gauge theory duality
• SL(2,R)/U(1) Supercoset and Elliptic Genera of Non-compact Calabi-Yau Manifolds
• Biorthogonal Quantum Systems
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Boundary States for the Rolling D-branes in NS5 Background
• D-branes in N=2 Liouville and its mirror
• The Virasoro Minimal String
• The Black Hole S-Matrix from Quantum Mechanics
• Liouville Quantum Gravity on the complex tori
• Hawking radiation of nonsingular black holes in two dimensions
• Duality and KPZ in Liouville Quantum Gravity
• The uses of the refined matrix model recursion
• Exact Bremsstrahlung and Effective Couplings
• Non-compact String Backgrounds and Non-rational CFT
• Conformal field theory on the plane
• Liouville Brownian motion
• Two perspectives of the 2D unit area quantum sphere and their equivalence
• Chiral Liouville Gravity
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Notes on Liouville Theory at c<=1
• Rolling Down the Throat in NS5-brane Background: The Case of Electrified D-Brane
• KPZ formula derived from Liouville heat kernel
• Towards physically motivated proofs of the Poincare' and geometrization conjectures
• Conifold Type Singularities, N=2 Liouville and SL(2;R)/U(1) Theories
• The unitary conformal field theory behind 2D Asymptotic Safety
• Continuum limit of fishnet graphs and AdS sigma model
• ZZ-Branes of N=2 Super-Liouville Theory
• Non-Perturbative Topological Strings And Conformal Blocks
• Notes on Matrix Models
• Bootstrapping 2D CFTs in the Semiclassical Limit
• Liouville heat kernel: regularity and bounds
• Non-BPS D-brane Near NS5-branes
• Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
• On boundary correlators in Liouville theory on AdS${}_2$
• SYK model with quadratic perturbations: the route to a non-Fermi-liquid
• Liouville Conformal Field Theories in Higher Dimensions
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• 3d gravity from Virasoro TQFT: Holography, wormholes and knots
• Noncritical M-Theory in 2+1 Dimensions as a Nonrelativistic Fermi Liquid
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• On AGT description of N=2 SCFT with N_f=4
• Schramm Loewner Evolution and Liouville Quantum Gravity
• Superstrings on AdS_2 and Superconformal Matrix Quantum Mechanics
• Quantum Gravity from Timelike Liouville theory
• Supercurrent, Supervirial and Superimprovement
• On the fusion matrix of the N=1 Neveu-Schwarz blocks
• The Stoyanovsky-Ribault-Teschner Map and String Scattering Amplitudes
• Supersymmetric Liouville theory in AdS${}_2$ and AdS/CFT
• Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
• On Perturbation theory improved by Strong coupling expansion
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• Liouville Theory on the Pseudosphere: Bulk-Boundary Structure Constant
• Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula
• Bootstrapping closed string field theory
• An action for the exact string black hole
• Integrability of boundary Liouville conformal field theory
• A brief review of the 2d/4d correspondences
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• Equivalence of Liouville measure and Gaussian free field
• On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation
• D-Brane Propagation in Two-Dimensional Black Hole Geometries
• The String Theory on AdS_3 as a Marginal Deformation of a Linear Dilaton Background
• A note on entanglement entropy for topological interfaces in RCFTs
• The Nothing at the Beginning of the Universe Made Precise
• Comments on 2D Type IIA String and Matrix Model
• Infinitely many inequivalent field theories from one Lagrangian
• On the heat kernel and the Dirichlet form of Liouville Brownian Motion
• 2D Quantum Gravity at One Loop with Liouville and Mabuchi Actions
• Extended Eigenstate Thermalization and the role of FZZT branes in the Schwarzian theory
• Extracting classical Lyapunov exponent from one-dimensional quantum mechanics
• Liouville theory without an action
• Riemann-Hilbert treatment of Liouville theory on the torus
• Geodesic distances in Liouville quantum gravity
• Quantum Cosmology Near Two Dimensions
• Accessory parameters for Liouville theory on the torus
• Non-abelian Toda theory on AdS${}_2$ and AdS${}_2$/CFT${}_2^{1/2}$ duality
• The complex Liouville string: the matrix integral
• Black holes and thermodynamics - The first half century
• D-branes and complex curves in c=1 string theory
• Long time black hole evaporation with bounded Hawking flux
• Microstates of a $2d$ Black Hole in string theory
• Fluctuations in non-conformal holographic plasma at criticality
• String Perturbation Theory on the Schwinger-Keldysh Time Contour
• Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT
• Integrability of Liouville theory: proof of the DOZZ Formula
• Hairpin-Branes and Tachyon-Paperclips in Holographic Backgrounds
• c < 1 String from Two Dimensional Black Holes
• Supersymmetric Biorthogonal Quantum Systems
• Classical and Quantum Integrability of 2D Dilaton Gravities in Euclidean space
• Long strings condensation and FZZT branes
• Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
• ADM reduction of Einstein action and black hole entropy
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Liouville Quantum Gravity and KPZ
• Matrix Model and Time-like Linear Dilaton Matter
• Spectral dimension of Liouville quantum gravity
• $Ad{S}_2$ holography is (non-)trivial for (non-)constant dilaton
• FZZ Algebra
• Liouville's Imaginary Shadow
• A Two-Dimensional String Cosmology
• $\mathcal{N}=1$ Liouville SCFT in Four Dimensions
• Comment on three-point function in AdS(3)/CFT(2)
• de Sitter Harmonies: Cosmological Spacetimes as Resonances
• On static solutions in 2D dilaton gravity with scalar matter
• Unitarity Meets Channel-Duality for Rolling / Decaying D-Branes
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Liouville gravity from Einstein gravity
• AFLT-type Selberg integrals
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Nesting statistics in the O(n) loop model on random planar maps
• A Worldsheet Description of Instant Folded Strings
• Hawking Effect in 2-D String Theory
• Another derivation of the geometrical KPZ relations
• Stochastic Ricci Flow on Compact Surfaces
• FZZ formula of boundary Liouville CFT via conformal welding
• The Torus One-Point Diagram in Two-Dimensional String Cosmology
• Cationic vacancies as defects in honeycomb lattices with modular symmetries
• Discrete Liouville equation and Teichmüller theory
• Duality in 2-dimensional dilaton gravity
• Proposal for the Open String Tachyon Effective Action in the Linear Dilaton Background
• Toda theory in AdS${}_2$ and $\mathcal{W}{A}_n$-algebra structure of boundary correlators
• Mabuchi spectrum from the minisuperspace
• Quantization of 2D Hořava gravity: non-projectable case
• Zamolodchikov relations and Liouville hierarchy in SL(2,R)_k WZNW model
• New scenarios for classical and quantum mechanical systems with position dependent mass
• Gauge Invariant Computable Quantities In Timelike Liouville Theory
• Semiclassical limit of the FZZT Liouville theory
• Discrete States in Light-Like Linear Dilaton Background
• Boundary Liouville Theory: Hamiltonian Description and Quantization
• Strings on AdS_2 and the High-Energy Limit of Noncritical M-Theory
• Renormalizability of Liouville Quantum Gravity at the Seiberg bound
• Conformal field theories on deformed spheres, anomalies, and supersymmetry
• 2D quantum gravity partition function on the fluctuating sphere
• Smoothness of correlation functions in Liouville Conformal Field Theory
• On the solution of Liouville equation
• Langlands duality in Liouville-H_3^+ WZNW correspondence
• c=1 from c<1: Bulk and boundary correlators
• Falling D0-Branes in 2D Superstring Theory
• Quantized cosmological constant in 1+1 dimensional quantum gravity with coupled scalar matter
• BRST cohomology of timelike Liouville theory
• Refined Cigar and Omega-deformed Conifold
• Electrostatics approach to closed string pair production from a decaying D-brane
• Odd Dimensional Nonlocal Liouville Conformal Field Theories
• Half-BPS Geometries and Thermodynamics of Free Fermions
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Black Hole - String Transition and Rolling D-brane
• ZZ boundary states and fragmented AdS2 spaces
• Can One Understand Black Hole Entropy without Knowing Much about Quantum Gravity?
• Crosscap states in N=2 Liouville theory
• Chameleonic equivalence postulate and wave function collapse
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• The ultrarelativistic limit of 2D dilaton gravity and its energy momentum tensor
• c-Recursion for multi-point superconformal blocks. NS sector
• FZZT Brane Relations in the Presence of Boundary Magnetic Fields
• Exact M-Theory Solutions, Integrable Systems, and Superalgebras
• Critical Non-Abelian Vortex and Holography for Little String Theory
• Notes on S-Matrix of Non-critical N=2 String
• Baby universes in 2d and 4d theories of quantum gravity
• A Note on Z_2 Symmetries of the KZ Equation
• Is cosmological constant screened in Liouville gravity with matter?
• Duality between 1+1 dimensional Maxwell-Dilaton gravity and Liouville field theory
• Large Strebel graphs and $(3,2)$ Liouville CFT
• Quantized Laplacian growth, III: On conformal field theories of Laplacian growth
• Disk one-point function for non-rational conformal theories
• Chern-Simons theory, exactly solvable models and free fermions at finite temperature
• Noncritical M-theory: Three Dimensions
• Non-renormalization for the Liouville wave function
• On the S-matrix of Liouville theory
• Universal Dynamics in Non-Orientable CFT${}_2$
• Pohlmeyer reduction for superstrings in AdS space
• Orientifolds in N=2 Liouville Theory and its Mirror
• Quantum gravity and the cosmological constant: lessons from two-dimensional dilaton gravity
• Refined topological amplitudes in N=1 flux compactification
• Gravitational action for a massive Majorana fermion in 2d quantum gravity
• Riemann-Hilbert treatment of Liouville theory on the torus: The general case
• Three-Point Function in Perturbed Liouville Gravity
• Renormalization of lattice field theories with infinite-range wavelets
• D-dualized D-brane
• Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
• Liouville Brownian motion at criticality
• Non-compact Mirror Bundles and (0,2) Liouville Theories
• 2d Sigma Models on Non-compact Calabi-Yau and $\mathcal{N}=2$ Liouville Theory
• Conformal Dimensions On Causal Random Geometry
• Liouville measure as a multiplicative cascade via level sets of the Gaussian free field
• Much ado about nothing: a treatise on empty and not-so-empty spacetimes
• On a relation between Liouville field theory and a two component scalar field theory passing through the random walk
• An SLE approach to four dimensional black hole microstate entropy
• On the Liouville 2D dilaton gravity models with sinh-Gordon matter
• Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties
• Critical Non-Abelian Vortex String and 2D N=2 Black Hole
• Noncritical M-theory and the Gross-Neveu model in 2+1 dimensions
• Warping effects in strongly perturbed metrics
• Diffusion of Brownian particles and Liouville field theory
• Boundary timelike Liouville theory: bulk 1-point & boundary 2-point functions
• Liouville perturbation theory for Laughlin state and Coulomb gas
• (0,2) Chiral Liouville Field Theory
• Schrödinger-like Dilaton Gravity
• Eternal Inflation with Liouville Cosmology
• Anisotropic scale invariant cosmology
• Vacuum States in 2D Tachyon Effective Action
• Higher Equations of Motion in N=2 Superconformal Liouville Field Theory
• The symmetric branes of the H4 WZW model
• A Family of Probability Distributions Consistent with the DOZZ Formula: Towards a Conjecture for the Law of 2D GMC
• Cylinder quantum field theories at small coupling
• Are Near $Ad{S}_2$ Spacetimes Dual to $Ad{S}_2$ Black Holes?
• If you want to cross singularity, wrap it!
• Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics
• The spatio-temporal statistical structure of the turbulent dissipation field and its stochastic representation as a Gaussian Multiplicative Chaos
• Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics