Lectures on 2D gravity and 2D string theory (TASI 1992)

Abstract

Emphasis is on 2d target space (c=1 coupled to gravity). Contents: 0. Introduction, Overview, and Purpose 1. Loops and States in Conformal Field Theory 2. 2D Euclidean Quantum Gravity I: Path Integral Approach 3. Brief Review of the Liouville Theory 4. 2D Euclidean Quantum Gravity II: Canonical Approach 5. 2D Critical String Theory 6. Discretized surfaces, matrix models, and the continuum limit 7. Matrix Model Technology I: Method of Orthogonal Polynomials 8. Matrix Model Technology II: Loops on the Lattice 9. Matrix Model Technology III: Free Fermions from the Lattice 10. Loops and States in Matrix Model Quantum Gravity 11. Loops and States in the $c=1$ Matrix Model 12. Fermi Sea Dynamics and Collective Field Theory 13. String scattering in two spacetime dimensions 14. Vertex Operator Calculations and Continuum Methods 15. Achievements, Disappointments, Future Prospects "if you read only one set of lecture notes this year, don't read these."

230 pages in harvmac l mode with 42 figures, all essential. WARNING: tex file is 472kb, figures another 285kb, also available only via anon ftp (as usual in hep-th/papers/9304), uses harvmac + epsf

References in corpus (21)

• 2D Gravity and Random Matrices
• Evanescent Black Holes
• Introduction to string field theory
• Closed String Field Theory: Quantum Action and the BV Master Equation
• W-symmetry in Conformal Field Theory
• Applied Conformal Field Theory
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• World Sheet and Space Time Physics in Two Dimensional (Super) String Theory
• Algebraic Structures and Differential Geometry in 2D String Theory
• Exact S-Matrix for 2D String Theory
• Multicritical Phases of the O(n) Model on a Random Lattice
• World-Sheet Geometry and Baby Universes in 2-D Quantum Gravity
• Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter
• Gauge Theory Formulation of the $c=1$ Matrix Model: Symmetries and Discrete States
• Classical Scattering in $1+1$ Dimensional String Theory
• Ward Identities in Two-Dimensional String Theory
• Gravity-Matter Couplings from Liouville Theory
• Gravitational Phase Transitions and the Sine-Gordon Model
• Black hole formation in $c=1$ String Field Theory
• Correlation functions from two-dimensional string Ward identities
• Unitarity Relations in c=1 Liouville Theory

Cited by in corpus (132)

• Holographic duality with a view toward many-body physics
• Superstrings and Topological Strings at Large N
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• Analytic Continuation of Liouville Theory
• Solving the Simplest Theory of Quantum Gravity
• Open string amplitudes and large order behavior in topological string theory
• JT gravity as a matrix integral
• The Holographic Renormalization Group
• Classical and Quantum D-branes in 2D String Theory
• Counting higher genus curves in a Calabi-Yau manifold
• LSZ in LST
• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Revisiting random tensor models at large N via the Schwinger-Dyson equations
• Long strings in two dimensional string theory and non-singlets in the matrix model
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• All solutions of the localization equations for N=2 quantum black hole entropy
• On Correlation Numbers in 2D Minimal Gravity and Matrix Models
• The Virasoro Minimal String
• Minimal String Theory
• The Black Hole S-Matrix from Quantum Mechanics
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Boundary Liouville Theory and 2D Quantum Gravity
• On Closed String Tachyon Dynamics
• Quantum moduli spaces from matrix models
• On the S-matrix of Type 0 String Theory
• Closed String Tachyon Condensation at c=1
• A new continuum limit of matrix models
• Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model
• Type 0 Strings in a 2-d Black Hole
• On the BCFT Description of Holes in the c=1 Matrix Model
• The unitary conformal field theory behind 2D Asymptotic Safety
• Non-Rational 2D Quantum Gravity: I. World Sheet CFT
• Little String Theory from a Double-Scaled Matrix Model
• D-brane Dynamics in the c=1 Matrix Model
• Effective action and phase transitions of scalar field on the fuzzy sphere
• The Large N Harmonic Oscillator as a String Theory
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• Boundary Ground Ring in 2D String Theory
• Observations On The Moduli Space Of Two Dimensional String Theory
• Noncritical M-Theory in 2+1 Dimensions as a Nonrelativistic Fermi Liquid
• Minimal Liouville Gravity correlation numbers from Douglas string equation
• Fuzzy spaces and new random matrix ensembles
• Spacelike boundaries from the c=1 Matrix Model
• Non-Perturbative String Equations for Type 0A
• Modeling Quantum Gravity Effects in Inflation
• On Perturbation theory improved by Strong coupling expansion
• Free particles from Brauer algebras in complex matrix models
• The Cap in the Hat: Unoriented 2D Strings and Matrix(-Vector) Models
• Boundary correlation numbers in one matrix model
• Non-Rational 2D Quantum Gravity II. Target Space CFT
• Complex matrix model duality
• Extended Toda lattice hierarchy, extended two-matrix model and c=1 string theory
• Indication for unsmooth horizon induced by quantum gravity interaction
• The decay of quantum D-branes
• Conifold geometries, topological strings and multi-matrix models
• Lifshitz-like systems and AdS null deformations
• Geodesic distances in Liouville quantum gravity
• Nonperturbative Effect in c=1 Noncritical String Theory and Penner Model
• The complex Liouville string: the matrix integral
• D-branes and complex curves in c=1 string theory
• Random matrix approach to scalar fields on fuzzy spaces
• The complex Liouville string: the worldsheet
• The Moduli Space and Phase Structure of Heterotic Strings in Two Dimensions
• Long strings condensation and FZZT branes
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• ADM reduction of Einstein action and black hole entropy
• Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT
• c < 1 String from Two Dimensional Black Holes
• The Multivalued Free-Field Maps of Liouville and Toda Gravities
• Liouville field theory for gluon saturation in QCD at high energy
• Quantum Gravity with Matter via Group Field Theory
• On the construction of the correlation numbers in Minimal Liouville Gravity
• Liouville Quantum Gravity and KPZ
• Boundary operators in minimal Liouville gravity and matrix models
• A geometric approach to free variable loop equations in discretized theories of 2D gravity
• Tachyon Backgrounds in 2D String Theory
• The emergence of noncommutative target space in noncritical string theory
• Bulk one-point function on disk in one-matrix model
• Deformations of JT Gravity via Topological Gravity and Applications
• Polymer quantization of CGHS model- I
• Non-Critical Superstrings from Four-Dimensional Gauge Theory
• Torus Amplitudes in Minimal Liouville Gravity and Matrix Models
• Matrix models and the gravitational interaction
• A localising AdS${}_3$ sigma model
• Higher Equations of Motion in Boundary Liouville Field Theory
• Nesting statistics in the O(n) loop model on random planar maps
• Boundary transitions of the O(n) model on a dynamical lattice
• Superluminal Travel Made Possible (in two dimensions)
• Isometry of AdS2 And The c=1 Matrix Model
• Gauge Invariant Computable Quantities In Timelike Liouville Theory
• On classical and semiclassical properties of the Liouville theory with defects
• Double Scaling Limits in Gauge Theories and Matrix Models
• Large N gauge theories and topological cigars
• Slavnov determinants, Yang-Mills structure constants, and discrete KP
• String Theory and Water Waves
• Boundary Description of Microstates of the Two-Dimensional Black Hole
• Monte Carlo studies of triangulated spherical surfaces in the two-dimensional space
• Hairpin Branes and D-Branes Behind the Horizon
• Semi-Classical Mechanics in Phase Space: The Quantum Target of Minimal Strings
• Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity
• ZZ boundary states and fragmented AdS2 spaces
• Matrix models for D-particle dynamics and the string/black hole transition
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• Multi-instantons in large N Matrix Quantum Mechanics
• Minimal String Theory is Logarithmic
• Irregular conformal block and its matrix model
• Virasoro constraints revisited
• Modular Integrals in Minimal Super Liouville Gravity
• Multi-boundary correlators in JT gravity
• Space-time filling branes in non critical (super) string theories
• A Note on Quantum Liouville Theory via Quantum Group; an Approach to Strong Coupling Liouville Theory
• Negative Screenings in Liouville Theory
• Unitary matrix integrals, symmetric polynomials, and long-range random walks
• The chiral SYK model in three-dimensional holography
• A proof of loop equations in 2d topological gravity
• A Riemann-Hilbert problem for equations of Painlevé type in the one matrix model with semi-classical potential
• Tachyon Effective Dynamics and de Sitter Vacua
• Variational ansatz for gaussian + Yang-Mills two matrix model compared with Monte-Carlo simulations in 't Hooft limit
• Time-dependent backgrounds of two dimensional string theory from the $c=1$ matrix model
• Primordial fluctuations in extended Liouville theory
• Noncritical M-theory and the Gross-Neveu model in 2+1 dimensions
• Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties
• Two dimensional general covariance from three dimensions
• Quenched free energy from spacetime D-branes
• A Note on Tachyon Moduli and Closed Strings
• Non-critical string, Liouville theory and geometric bootstrap hypothesis
• Noncommutativity in two-matrix model extension of one-dimensional topological gravity
• Vacuum States in 2D Tachyon Effective Action
• Two-dimensional Liouville Gravity Theory with Non-Trivial Classical Background
• Large-N Limit as a Classical Limit: Baryon in Two-Dimensional QCD and Multi-Matrix Models