Applied Conformal Field Theory

Abstract

These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in 2 dimensions 3. The central charge and the Virasoro algebra 4. Kac determinant and unitarity 5. Identication of m = 3 with the critical Ising model 6. Free bosons and fermions 7. Free fermions on a torus 8. Free bosons on a torus 9. Affine Kac-Moody algebras and coset constructions 10. Advanced applications

Lectures given at Les Houches summer session, Jun 28 -- Aug 5, 1988

Cited by in corpus (273)

• Entanglement in quantum critical phenomena
• Geometric and Renormalized Entropy in Conformal Field Theory
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• D-branes and Deformation Quantization
• The Analytic Bootstrap and AdS Superhorizon Locality
• Two-dimensional conformal field theory and the butterfly effect
• Liouville Field Theory -- A decade after the revolution
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Quark confinement and the bosonic string
• K3 Surfaces and String Duality
• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
• String Theory on Calabi-Yau Manifolds
• AdS${}_2$ holography and the SYK model
• Entanglement entropy in the Lipkin-Meshkov-Glick model
• Lectures on 2D gravity and 2D string theory (TASI 1992)
• Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories
• Entanglement Scrambling in 2d Conformal Field Theory
• Introduction to Superstring Theory
• D-branes as Tachyon Lumps in String Field Theory
• Critical Casimir forces in cellular membranes
• BMS Particles in Three Dimensions
• A Web of 2d Dualities: ${\mathbf{Z}}_2$ Gauge Fields and Arf Invariants
• Lectures on Quantum Black Holes
• String Consistency for Unified Model Building
• Exact Matrix Product States for Quantum Hall Wave Functions
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• AdS Field Theory from Conformal Field Theory
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• Non-unitary Conformal Field Theory and Logarithmic Operators for Disordered Systems
• Fusion of conformal interfaces
• String compactifications on Calabi-Yau stacks
• Long-range entanglement from measuring symmetry-protected topological phases
• Universal geometric entanglement close to quantum phase transitions
• Strings on Curved Spacetimes: Black Holes, Torsion, and Duality
• Non-compact Calabi--Yau Manifolds and Localized Gravity
• A theory of deconfined pseudo-criticality
• Correlation Functions in Non-Relativistic Holography
• Strings on a Cone and Black Hole Entropy
• Conformal Field Theories, Representations and Lattice Constructions
• Modular Invariant Partition Functions in the Quantum Hall Effect
• Hawking from Catalan
• Entanglement entropy of two disjoint intervals in c=1 theories
• The Kerr/CFT correspondence and its extensions: a comprehensive review
• Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal Models
• Notes on gauging noneffective group actions
• Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
• Half the entanglement in critical systems is distillable from a single specimen
• Superconformal Symmetry in Three-dimensions
• Lectures on Orientifolds and Duality
• String Universality for Permutation Orbifolds
• MHV Gluon Scattering Amplitudes from Celestial Current Algebras
• Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$
• 2004 TASI Lectures on Supersymmetry Breaking
• Explicit Construction of Yang-Mills Instantons on ALE Spaces
• W-Infinity and String Theory
• Spin structures and entanglement of two disjoint intervals in conformal field theories
• Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics
• Testing the Generalized Second Law in 1+1 dimensional Conformal Vacua: An Argument for the Causal Horizon
• Theory of d-density wave viewed from a vertex model and its implications
• Warped Weyl fermion partition functions
• Pivot Hamiltonians as generators of symmetry and entanglement
• Renyi entropies of free bosons on the torus and holography
• Y-junction of superconducting Josephson chains
• On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine
• Supersymmetric Protection and the Swampland
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• The string partition function in Hull's doubled formalism
• Lectures on W algebras and W gravity
• Fermionic Matrix Models
• From Fixed Points to the Fifth Dimension
• Conformal Quasicrystals and Holography
• Entanglement and majorization in (1+1)-dimensional quantum systems
• Little String Amplitudes (and the Unreasonable Effectiveness of 6D SYM)
• Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Microscopic characterization of Ising conformal field theory in Rydberg chains
• Boundary Conformal Field Theory and Tunneling of Edge Quasiparticles in non-Abelian Topological States
• Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks
• Effective Boundary Field Theory for a Josephson Junction Chain with a Weak Link
• Undoing decomposition
• Duality Symmetries and Noncommutative Geometry of String Spacetime
• Strange Metals in One Spatial Dimension
• Four Lectures on Analytic Solutions in Open String Field Theory
• Two-Loop Superstrings on Orbifold Compactifications
• Noncommutative Solitons on Orbifolds
• Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• On the Construction of Asymmetric Orbifold Models
• Equivariant Localization of Path Integrals
• Entanglement in gapless resonating valence bond states
• Normal form for renormalization groups
• Doubly Special Relativity in Position Space Starting from the Conformal Group
• Beyond Logarithmic Corrections to Cardy Formula
• Compactification, Geometry and Duality: N=2
• Multipartitioning topological phases by vertex states and quantum entanglement
• Non-planar Anomalous Dimensions in the sl(2) Sector
• Ghost Systems: A Vertex Algebra Point of View
• Entanglement Entropy, Conformal Invariance and the Critical Behavior of the Anisotropic Spin-S Heisenberg Chains: A DMRG study
• $W_{1+\infty }$ Dynamics of Edge Excitations in the Quantum Hall Effect
• Quantum symmetries in orbifolds and decomposition
• Conformal bootstrap for percolation and polymers
• Inter edge Tunneling in Quantum Hall Line Junctions
• Les Houches Lectures on Fields, Strings and Duality
• Lectures on Conformal Field Theory
• Isomonodromic Properties of the Seiberg-Witten Solution
• Semiclassical Scaling Functions of Sine--Gordon Model
• Competing Boundary Interactions in a Josephson Junction Network with an Impurity
• Conformal Field Theories with Sporadic Group Symmetry
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence
• Heterotic Flux Vacua from Hybrid Linear Models
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Gravity/CFT correspondence for three dimensional Einstein gravity with a conformal scalar field
• Explicit monodromy of Moore-Read wave functions on a torus
• On the complete classification of the unitary N=2 minimal superconformal field theories
• Abelian and Non-abelian D-brane Effective Actions
• Large Interval Limit of Rényi Entropy At High Temperature
• A few Ricci-flat stacks as phases of exotic GLSM's
• Two-point functions with an invariant Planck scale and thermal effects
• Stringy profiles of gauge field tadpoles near orbifold singularities: I. heterotic string calculations
• TASI Lectures on Perturbative String Theories
• Note on Chern-Simons Term Correction to Holographic Entanglement Entropy
• Two-dimensional models as testing ground for principles and concepts of local quantum physics
• Group Averaging of massless scalar fields in 1+1 de Sitter
• Conformal scaling and the size of $m$-hadrons
• Numerical Study of Hierarchical Hall Edge States on the Disk Geometry
• The $W_{1+\infty }$ effective theory of the Calogero- Sutherland model and Luttinger systems.
• Extreme boundary conditions and random tilings
• Non-periodic Ising quantum chains and conformal invariance
• The Moduli Space of N = 2 Superconformal Field Theories
• Paired states on a torus
• A generalization of decomposition in orbifolds
• Finite size effects in the spin-1 XXZ and supersymmetric sine-Gordon models with Dirichlet boundary conditions
• The Real-Time Correlation Function of Floquet Conformal Fields
• The nu=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between abelian and non-abelian statistics
• Gaplessness of the Gaffnian
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
• Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields
• A common limit of super Liouville theory and minimal models
• A study of truncation effects in boundary flows of the Ising model on a strip
• Exact solution and finite size properties of the $U_q[osp(2|2m)]$ vertex model
• Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models
• Bosonic String Quantization in Static Gauge
• Continuous tensor network renormalization for quantum fields
• Comments on MHV Tree Amplitudes for Conformal Supergravitons from Topological B-Model
• Virasoro-type Symmetries in Solvable Models
• Bootstrap Methods in 1+1-Dimensional Quantum Field Theories: The Homogeneous Sine-Gordon Models
• Tensor networks as conformal transformations
• Characterizing the quantum field theory vacuum using temporal Matrix Product states
• Low-Lying States of the Six-Dimensional Fractional Superstring
• A geometric approach to free variable loop equations in discretized theories of 2D gravity
• Finite and Infinite W Algebras and their Applications
• Calculus on manifolds of conformal maps and CFT
• 2D Superconductivity: Classification of Universality Classes by Infinite Symmetry
• The representations of Temperley-Lieb-Jones algebras
• Algebraic approach to parafermionic conformal field theories
• Orbifold Compactifications with continuous Wilson lines
• Third and Higher Order NFPA Twisted Constructions of Conformal Field Theories from Lattices
• The onset of quantum chaos in disordered CFTs
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Aspects of M-Theory Brane Interactions and String Theory Symmetries
• Spectra of Heterotic Strings on Orbifolds
• Moyal Noncommutative Integrability and the Burgers-KdV Mapping
• Snapshots of Conformal Field Theory
• Matrix models of 2d gravity
• On conjectured local generalizations of anisotropic scale invariance and their implications
• Correlation functions of sourced gravitational waves in inflationary scalar vector models. A symmetry based approach
• Conformal loop ensembles and the stress-energy tensor. II. Construction of the stress-energy tensor
• Refining the Shifted Topological Vertex
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Cloning SO(N) level 2
• Random loops and conformal field theory
• Random Surfaces and Lattice Gravity
• The Spectra of Supersymmetric States in String Theory
• BUSSTEPP Lectures on String Theory
• On Nontrivial Solutions around a Marginal Solution in Cubic Superstring Field Theory
• Spin-Statistics Theorem in Path Integral Formulation
• Some tree-level string amplitudes in the NSR formalism
• Resonant two-site tunnelling dynamics of bosons in a tilted optical superlattice
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Periodically driven perturbed CFTs: the sine-Gordon model
• $\mathcal{N}=(3,3)$ holography on ${\mathrm{AdS}}_3\times ({\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1)/{\mathbb{Z}}_2$
• Space and time dependent scaling of numbers in mathematical structures: Effects on physical and geometric quantities
• Admissible sl(2/1) Characters and Parafermions
• Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of nu = 1/(2p+1) quantum Hall sequences
• Fusion Algebras and Characters of Rational Conformal Field Theories
• Coadjoint Orbits and Conformal Field Theory
• Virasoro Representations on (Diff S1)/S1 Coadjoint Orbits
• Virasoro blocks at large exchange dimension
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Tachyon instability and Kondo type models
• Covariant Vertex Operators for Cosmic Strings
• A Monte Carlo method for critical systems in infinite volume: the planar Ising model
• Effective Field Theory and Integrability in Two-Dimensional Mott Transition
• The Goldstone Equivalence Theorem and AdS/CFT
• Boundary CFT and tensor network approach to surface critical phenomena of the tricritical 3-state Potts model
• Four-dimensional conformal field theory using quaternions
• Topological gauge theories with antisymmetric tensor matter fields
• Lattice Integrals of Motion of the Ising Model on the Cylinder
• On the Free Energy of Solvable lattice Models
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs
• Conformal invariance in the three dimensional (3D) Ising model and quaternionic geometric phase in quaternionic Hilbert space
• Twistors, strings and supersymmetric gauge theories
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• DLCQ Strings, Twist Fields and One-Loop Correlators on a Permutation Orbifold
• Hypotrochoids in conformal restriction systems and Virasoro descendants
• Algebraic K-Theory and Partition Functions in Conformal Field Theory
• Transport in a One-Dimensional Hyperconductor
• Relevant boundary perturbations of CFT: A case study
• Lie algebraic structures in integrable models, affine Toda field theory
• The 3D Yang-Mills system. Lecture notes on the Karabali-Nair theory
• Topics in String Theory and Quantum Gravity
• Dynamics of D-brane Black Holes
• The Moyal Momentum algebra applied to (theta)-deformed 2d conformal models and KdV-hierarchies
• Classification of the Chiral Z_2 x Z_2 Heterotic String Models
• Lectures on Naturalness, String Landscape and Multiverse
• Lee-Yang Model in Presence of Defects
• Principal fiber bundle description of number scaling for scalars and vectors: Application to gauge theory
• The Orbifolds of N=2 Superconformal Theories with c=3
• Issues on tadpoles and vacuum redefinitions in String Theory
• WZW model based on the extended de Sitter group
• A Study of Two Dimensional String Theory (PhD Thesis)
• Fixed points of (0,2) Landau-Ginzburg renormalization group flows and the chiral algebra
• On the harmonic superspace language adapted to the Gelfand-Dickey algebra of differential operators
• Deformations of anti-de Sitter black holes
• Vertex--Operatoren, Darstellungen der Virasoro--Algebra und konforme Quantenfeldtheorie
• Geometric and computational aspects of chiral topological quantum matter
• Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models
• Black Hole Evaporation. A Survey
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• On the AdS/CFT correspondence and quantum entanglement
• Late-time correlators in semiclassical particle-black hole scattering
• Real-Time Ramsey Interferometry in Fractional Quantum Hall States
• BKT transition and level spectroscopy
• Dynamical Zero Modes and Criticality in Continuous Light Cone Quantization of Phi^{4}_{1+1}
• Boundary effects in two-dimensional critical and off-critical systems
• Pasquier Models at c=1: Cylinder Partition Functions and the role of the Affine Coxeter Element
• Non-perturbative Treatments of the Bosonic String and the Axion with Cosmological Implications
• Non-locally Regularized Field-Antifield Quantization of the Chiral Schwinger Model
• Extended conformal symmetry of the one-dimensional Bose gas
• Relating Schwarzschild Black Holes to Branes-Antibranes
• One-loop and D-instanton corrections to the effective action of open string models
• Continuous Symmetries of Lattice Conformal Field Theories and their $Z_2$-Orbifolds
• A non-commuting twist in the partition function
• Structure of Lorentzian algebras and Conformal Field Theory
• Aspects of W_\INFTY Symmetry
• Agujeros negros clasicos y cuanticos en teoria de cuerdas
• Universality in Non-Equilibrium Quantum Systems
• Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories
• c = 1 conformal field theory and the fractional quantum Hall effect
• Critical points of 2d disordered Dirac fermions: the Quantum Hall Transitions revisited
• BRST invariant branching functions of G/H coset models
• Topological defects in string theory orbifolds with target spaces $\mathbb{C}/{\mathbb{Z}}_N$ and $S^1/{\mathbb{Z}}_2$
• L'algebre des symetries quantiques d'Ocneanu et la classification des systemes conformes a 2D
• Hidden symmetries and nonlinear (super)algebras
• Superstrings beyond one loop
• Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application
• A noncommutative anomaly through Seiberg-Witten map and non-locally regularized BV quantization
• The (Super)String Theories' Problems
• Tensor network states for the description of quantum many-body systems
• On the $D_n$ Spin Vertex Models for Odd $n$
• Entanglement and Excitations in Gauge/Gravity Duality
• Introductory lecture notes on the Karabali-Nair theory
• BMS in higher space-time dimensions and Non-relativistic BMS
• Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance
• Chern-Simons Gauge Invariance and Boundary Conformal Fields
• The extended conformal theory of the Calogero-Sutherland model
• Entanglement and its applications in systems with many degrees of freedom
• Existence of conserved quantities and their algebra in curved spacetime
• Heterotic $D=2(1/3,0)$ Susy Models
• F-Susy And The Three States Potts Model
• Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations