EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions

Abstract

This is a writeup of lectures given at the EPFL Lausanne in the fall of 2012. The topics covered: physical foundations of conformal symmetry, conformal kinematics, radial quantization and the OPE, and a very basic introduction to conformal bootstrap.

68 pages; v2 - misprints corrected

References in corpus (4)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• TASI Lectures on the Conformal Bootstrap
• A Semidefinite Program Solver for the Conformal Bootstrap
• Comments on Determinant Formulas for General CFTs

Cited by in corpus (191)

• A Mellin space approach to the conformal bootstrap
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• Operator bases, $S$-matrices, and their partition functions
• Intrinsic and emergent anomalies at deconfined critical points
• Semiclassics, Goldstone Bosons and CFT data
• Analyticity and Unitarity for Cosmological Correlators
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Bootstrapping the half-BPS line defect
• Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• The Epsilon Expansion Meets Semiclassics
• A tauberian theorem for the conformal bootstrap
• Multipoint Conformal Blocks in the Comb Channel
• Deformation quantization and superconformal symmetry in three dimensions
• The 3d Stress-Tensor Bootstrap
• Conformal dimensions via large charge expansion
• A Holographic Derivation of the Weak Gravity Conjecture
• On duality of color and kinematics in (A)dS momentum space
• Universality at large transverse spin in defect CFT
• Crossing Symmetry in Alpha Space
• TASI lectures on AdS/CFT
• Bulk Phase Shift, CFT Regge Limit and Einstein Gravity
• The critical O(N) CFT: Methods and conformal data
• Conformal Carroll Scalars with Boosts
• The Random-Bond Ising Model in 2.01 and 3 Dimensions
• The $O(N)$ Model in $4<d<6$: Instantons and Complex CFTs
• The Mellin Formalism for Boundary CFT${}_d$
• Momentum space approach to crossing symmetric CFT correlators
• A conformal bootstrap approach to critical percolation in two dimensions
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• ETH and Modular Invariance of 2D CFTs
• Analytic Euclidean Bootstrap
• The Black Hole S-Matrix from Quantum Mechanics
• Bootstrapping the long-range Ising model in three dimensions
• Free box^k Scalar Conformal Field Theory
• Universal correlation functions in rank 1 SCFTs
• Dimensional Reduction for Conformal Blocks
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Decoding a Three-Dimensional Conformal Manifold
• Constraints on Flavored 2d CFT Partition Functions
• The M-theory Archipelago
• Exact Correlation Functions in Conformal Fishnet Theory
• Operator Dimensions from Moduli
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• The nuts and bolts of the BMS Bootstrap
• String Field Theory -- A Modern Introduction
• Black Holes, Heavy States, Phase Shift and Anomalous Dimensions
• Universality of Quantum Information in Chaotic CFTs
• Anatomy of Geodesic Witten Diagrams
• Witten Diagrams for Torus Conformal Blocks
• Anomalous Symmetries End at the Boundary
• Positivity bounds on effective field theories with spontaneously broken Lorentz invariance
• Geodesic Diagrams, Gravitational Interactions & OPE Structures
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• Radial coordinates for defect CFTs
• A conformal block Farey tail
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories
• Anomalous dimensions at finite conformal spin from OPE inversion
• On the Positive Geometry of Conformal Field Theory
• Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks
• Basic introduction to higher-spin theories
• High-dimensional sphere packing and the modular bootstrap
• Black Holes and Conformal Regge Bootstrap
• Momentum space spinning correlators and higher spin equations in three dimensions
• Thermal Conformal Blocks
• Holographic OPE Coefficients from AdS Black Holes with Matters
• Cut-touching linear functionals in the conformal bootstrap
• Transition from a Dirac spin liquid to an antiferromagnet: Monopoles in a QED3-Gross-Neveu theory
• Leading Multi-Stress Tensors and Conformal Bootstrap
• Spinning Geodesic Witten Diagrams
• An AdS/EFT correspondence at large charge
• Thermalization in Large-N CFTs
• Constraining momentum space correlators using slightly broken higher spin symmetry
• New Methods for Conformal Correlation Functions
• On Information Loss in AdS${}_3$/CFT${}_2$
• Conformal bootstrap for percolation and polymers
• Action principle for OPE
• Lattice Dirac Fermions on a Simplicial Riemannian Manifold
• Towards Spinning Mellin Amplitudes
• AdS/CFT Correspondence in Operator Formalism
• Aspects of Non-Relativistic Quantum Field Theories
• Dynamical response near quantum critical points
• Conformal Boundary Condition and Massive Gravitons in AdS/BCFT
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Transition between algebraic and ${\mathbb{Z}}_2$ quantum spin liquids at large $N$
• Bulk Locality in AdS/CFT Correspondence
• Resummation at finite conformal spin
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Extremal bootstrapping: go with the flow
• Lattice ${\varphi }^4$ Field Theory on Riemann Manifolds: Numerical Tests for the 2-d Ising CFT on ${\mathbb{S}}^2$
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Scale invariant solids
• Mixed OPEs in $\mathcal{N}=2$ Superconformal Theories
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Schrödinger symmetry: a historical review
• Perturbative linearization of super-Yang-Mills theories in general gauges
• Conformal Correlation functions in four dimensions from Quaternionic Lauricella system
• Scale without conformal invariance in membrane theory
• N=4 super Yang-Mills correlators without anti-commuting variables
• Conformal invariance of TMD rapidity evolution
• Scale-Free Networks beyond Power-Law Degree Distribution
• Ising model close to $d=2$
• Efficient Rules for All Conformal Blocks
• Black Hole Horizons as Patternless Binary Messages and Markers of Dimensionality
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• Conformal Bootstrap Signatures of the Tricritical Ising Universality Class
• De Sitter Special Relativity as a Possible Reason for Conformal Symmetry and Confinement in QCD
• Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly
• One-Dimensional Sectors From the Squashed Three-Sphere
• Lightcone expansions of conformal blocks in closed form
• Mixed Graviton and Scalar Bispectra in the EFT of Inflation: Soft Limits and Boostless Bootstrap
• An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• Conformal partial waves in momentum space
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• Numerical tests of the large charge expansion
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• Missing Corner in the Sky: Massless Three-Point Celestial Amplitudes
• Classical Limit of Large N Gauge Theories with Conformal Symmetry
• Loops in dS/CFT
• Sub-leading conformal dimensions at the O(4) Wilson-Fisher fixed point
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Scale without Conformal Invariance in Dipolar Ferromagnets
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Superfluids, vortices and spinning charged operators in 4d CFT
• Dark Matter from a Conformal Dark Sector
• More on the operator-state map in non-relativistic CFTs
• The Analytic Bootstrap in Fermionic CFTs
• Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$
• A Note on Commutation Relation in Conformal Field Theory
• On fast quenches and spinning correlators
• Bootstrapping (D, D) Conformal Matter
• Conformal Bootstrap Deformations
• Conformal Fields from Neural Networks
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Wilsonian renormalisation of CFT correlation functions: Field theory
• Meta-Schrödinger invariance
• Supersymmetric Galilean conformal blocks
• Determinant Formula for Parabolic Verma Modules of Lie Superalgebras
• Bulk reconstruction in AdS and Gel'fand-Graev-Radon Transform
• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• Wilson Action for the $O(N)$ Model
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Bananas are Unparticles: Differential Equations and Cosmological Bootstrap
• Casimir Forces in CFT with Defects and Boundaries
• RG flows on $S^d$ and Hamiltonian truncation
• ${\beta }_{IR}^{\prime }$ at an Infrared Fixed Point in Chiral Gauge Theories
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions
• CFT in Conformally Flat Spacetimes
• The conformal N-point scalar correlator in coordinate space
• Three-dimensional real space renormalization group with well-controlled approximations
• Mellin Bootstrap for Scalars in Generic Dimension
• Higher-dimensional field theories from type II supergravity
• Destabilization of U(1) Dirac spin-liquids on two dimensional non-bipartite lattices by quenched disorder
• Double-trace deformation in Keldysh field theory
• Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model
• Strongly Coupled Sectors in Inflation: Gapless Theories and Unparticles
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Bound on the central charge of CFTs in large dimension
• Universal Dynamics in Non-Orientable CFT${}_2$
• autoboot: A generator of bootstrap equations with global symmetry
• The gravity dual of Lorentzian OPE blocks
• Magnetization profiles at the upper critical dimension as solutions of the integer Yamabe problem
• The geometry of optimal functionals
• Quantum Groups as Global Symmetries II. Coulomb Gas Construction
• Monopole hierarchy in transitions out of a Dirac spin liquid
• Probing Black Hole Microstate Evolution with Networks and Random Walks
• Simple Bulk Reconstruction in AdS/CFT Correspondence
• FeynGrav and Recent Progress in Computational Perturbative Quantum Gravity
• Finite Cutoff CFT's and Composite Operators
• Superconformal Block from Holographic Geometry
• The Operator Product Expansion in Quantum Field Theory
• Bootstrapping mixed correlators in the 2D Ising model
• CFTs on curved spaces
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models
• The Operator Product Expansion for Radial Lattice Quantization of 3D ${\varphi }^4$ Theory
• How to Succeed at Witten Diagram Recursions without Really Trying
• On Gluing CFT Correlators to Higher-Spin Amplitudes in AdS
• Reconstructing the boundary of AdS from an infrared defect
• Cosmology from Strong Interactions
• On the equivalence of two definitions of conformal primary fields in d > 2 dimensions
• Maximally Supersymmetric AdS Solutions in Gauged Supergravity
• Two Dimensional Conformal Field Theory and a Primer to Chiral Algebras
• Cardy's Conjecture and the Spectrum of Infrared Strongly-Coupled Quantum Field Theories
• Regularization of energy-momentum tensor correlators and parity-odd terms
• Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance