The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

Abstract

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible both due to significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world record determinations of critical exponents and correlation function coefficients in the Ising and $O(N)$ models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.

81 pages, double column, 58 figures; v3: updated references, minor typos corrected

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• Conformal Field Theories in Fractional Dimensions
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• Recursion Relations for Conformal Blocks
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• Chiral algebras of class S
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• Universal anomalous dimensions at large spin and large twist
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Conformal Bootstrap Dashing Hopes of Emergent Symmetry
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Long-range critical exponents near the short-range crossover
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• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
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• On Four-Point Functions of Half-BPS Operators in General Dimensions
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• Solving CFTs with Weakly Broken Higher Spin Symmetry
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• Stress-tensor OPE in N=2 Superconformal Theories
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• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
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• Scale and conformal invariance in field theory: a physical counterexample
• Crossing Symmetry in Alpha Space
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• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• Conformal Collider Physics from the Lightcone Bootstrap
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Holographic Reconstruction of AdS Exchanges from Crossing Symmetry
• More Holography from Conformal Field Theory
• Covariant Approaches to Superconformal Blocks
• Conformal Bootstrap in the Regge Limit
• The superconformal bootstrap for structure constants
• Hawking from Catalan
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• Towards Bootstrapping QED${}_3$
• A Numerical Approach to Virasoro Blocks and the Information Paradox
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• The Random-Bond Ising Model in 2.01 and 3 Dimensions
• Radial expansion for spinning conformal blocks
• Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions
• Solving M-theory with the Conformal Bootstrap
• Higher-point conformal blocks and entanglement entropy in heavy states
• The Mellin Formalism for Boundary CFT${}_d$
• Chiral Algebras for Trinion Theories
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• Displacement Operators and Constraints on Boundary Central Charges
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• Mellin space bootstrap for global symmetry
• A conformal bootstrap approach to critical percolation in two dimensions
• Seed Conformal Blocks in 4D CFT
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• On 4d rank-one N=3 superconformal field theories
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• Analysis of a Dilaton EFT for Lattice Data
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• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• Multipoint correlators of conformal field theories: implications for quantum critical transport
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
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• Monopoles in CP(N-1) model via the state-operator correspondence
• Bootstrapping critical Ising model on three-dimensional real projective space
• From global to heavy-light: 5-point conformal blocks
• Current OPEs in Superconformal Theories
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• From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models
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• (2,2) Superconformal Bootstrap in Two Dimensions
• JuliBootS: a hands-on guide to the conformal bootstrap
• Conformal Field Theories and Deep Inelastic Scattering
• On critical exponents without Feynman diagrams
• Macdonald Index and Chiral Algebra
• Phase transitions in 3D loop models and the $C{P}^{n-1}$ $\sigma$ model
• On the four-point function of the stress-energy tensors in a CFT
• Bounds on Operator Dimensions in 2D Conformal Field Theories
• Accidental Symmetries and the Conformal Bootstrap
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• Strong dynamics, composite Higgs and the conformal window
• Superembedding methods for 4d N=1 SCFTs
• Higgs criticality in a two-dimensional metal
• Anomalous dimensions at finite conformal spin from OPE inversion
• Fermion-Scalar Conformal Blocks
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Scale Anomalies, States, and Rates in Conformal Field Theory
• More on analytic bootstrap for O(N) models
• In search of conformal theories
• Spinning Geodesic Witten Diagrams
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• Superembedding Methods for Current Superfields
• Bootstrapping 2D CFTs in the Semiclassical Limit
• Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
• Bootstrap bound for conformal multi-flavor QCD on lattice
• $\epsilon$-Expansion in the Gross-Neveu CFT
• Looking behind the Standard Model with lattice gauge theory
• Chiral Algebras, Localization and Surface Defects
• Exploring the Minimal 4D $\mathcal{N}=1$ SCFT
• The finite-temperature chiral transition in QCD with adjoint fermions
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Three-dimensional antiferromagnetic CP(N-1) models
• Holographic duals of large-c torus conformal blocks
• Universal Bounds on Operator Dimensions from the Average Null Energy Condition
• OPE convergence in non-relativistic conformal field theories
• On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories
• Conformal Bootstrap in Embedding Space
• Superconformal partial waves in Grassmannian field theories
• Geodesic Witten diagrams with an external spinning field
• On Calculation of 1/n Expansions of Critical Exponents in the Gross-Neveu Model with the Conformal Technique
• Inverse Bootstrapping Conformal Field Theories
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• Revisiting N=4 superconformal blocks
• The enigma of the pseudogap phase of the cuprate superconductors
• Global Conformal Invariance in D-dimensions and Logarithmic Correlation Functions
• Superconformal Blocks for SCFTs with Eight Supercharges
• Bootstrapping the $\cN=1$ SCFT in three dimensions
• Constraining quantum critical dynamics: 2+1D Ising model and beyond
• Operator product expansion for conformal defects
• A search for minimal 4d N=1 SCFT
• The unitary subsector of generalized minimal models
• Non-gaussianity of the critical 3d Ising model
• On conformal correlators and blocks with spinors in general dimensions
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Criticality of O(N) symmetric models in the presence of discrete gauge symmetries
• Global Structure of Conformal Theories in the SU(3) Gauge Theory
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• Crossing symmetry and Higher spin towers
• Comments on Determinant Formulas for General CFTs
• Mixed OPEs in $\mathcal{N}=2$ Superconformal Theories
• Anomalous dimensions on the lattice
• Various semiclassical limits of torus conformal blocks
• Two-point functions of conformal primary operators in $\mathcal{N}=1$ superconformal theories
• A Small Deformation of a Simple Theory
• Quantum Integrable Systems from Conformal Blocks
• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap
• Reflections on Conformal Spectra
• Geodesic Witten diagrams with anti-symmetric exchange
• Perturbative search for dead-end CFTs
• Anomalous dimensions of spinning operators from conformal symmetry
• Geodesic description of Heavy-Light Virasoro blocks
• IR fixed points in $SU(3)$ gauge Theories
• Bounds on CFTs with $W_3$ algebras and AdS${}_3$ higher spin theories
• Conformal perturbation of off-critical correlators in the 3D Ising universality class
• The Analytic Bootstrap in Fermionic CFTs
• Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
• The Conformal Characters
• Spectral sum rules for conformal field theories in arbitrary dimensions
• OPE inversion in Mellin space
• Testing Fermion Universality at a Conformal Fixed Point

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• Critical Ising Model in Varying Dimension by Conformal Bootstrap
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• Modular Constraints on Superconformal Field Theories
• Bootstrapping 4d $\mathcal{N}=2$ gauge theories: the case of SQCD
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Scrambling and decoding the charged quantum information
• Conformal Boundary Condition and Massive Gravitons in AdS/BCFT
• Anomalous fractal scaling in two-dimensional electric networks
• Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising Model
• Towards Feynman rules for conformal blocks
• Gentle introduction to rigorous Renormalization Group: a worked fermionic example
• Searching for continuous phase transitions in 5D SU(2) lattice gauge theory
• Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap
• Conformal dispersion relations for defects and boundaries
• On Galilean conformal bootstrap
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Swampland Conditions for Higher Derivative Couplings from CFT
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• Seeking SUSY fixed points in the $4-\epsilon$ expansion
• Lightcone Commutator and Stress-Tensor Exchange in $d>2$ CFTs
• Conformal Floquet dynamics with a continuous drive protocol
• Non-Gaussianities in Collider Energy Flux
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• Three-dimensional $O(N)$-invariant ${\varphi }^4$ models at criticality for $N\ge 4$
• Evolution of entanglement entropy at SU($N$) deconfined quantum critical points
• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• Charting the space of 3D CFTs with a continuous global symmetry
• Holographic solar systems and hydrogen atoms: non-relativistic physics in AdS and its CFT dual
• Symmetries and spectral statistics in chaotic conformal field theories
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• Relevance in the Renormalization Group and in Information Theory
• Bootstrapping traceless symmetric $O(N)$ scalars
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• An invitation to the principal series
• Polyakov-Mellin Bootstrap for AdS loops
• blocks_3d: Software for general 3d conformal blocks
• Resurgence, Conformal Blocks, and the Sum over Geometries in Quantum Gravity
• Toward a 3d Ising model with a weakly-coupled string theory dual
• The Hydrohedron: Bootstrapping Relativistic Hydrodynamics
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• Confining Strings, Infinite Statistics and Integrability
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Conformal Freeze-In of Dark Matter
• CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD
• The Shadow Formalism of Galilean CFT${}_2$
• Conformal Bootstrap near the edge
• Conformal Correlation functions in four dimensions from Quaternionic Lauricella system
• AdS/CFT Unitarity at Higher Loops: High-Energy String Scattering
• Looking through the QCD Conformal Window with Perturbation Theory
• Casimir Energy and Modularity in Higher-dimensional Conformal Field Theories
• Taming Dyson-Schwinger equations with null states
• Bootstrapping the Kronig-Penney Model
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Critical properties of the Néel/algebraic-spin-liquid transition
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• Scale without conformal invariance in membrane theory
• Exploring $SU(N)$ adjoint correlators in $3d$
• Closed-form expression for cross-channel conformal blocks near the lightcone
• Towards the higher point holographic momentum space amplitudes
• Certified algorithms for equilibrium states of local quantum Hamiltonians
• Thermal CFTs in momentum space
• Positive geometry in the diagonal limit of the conformal bootstrap
• Conformal Bootstrap Signatures of the Tricritical Ising Universality Class
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
• Dispersive Sum Rules in AdS${}_2$
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• Bootstrap Bounds on Closed Einstein Manifolds
• Bounds on multiscalar CFTs in the epsilon expansion
• Feynman Rules for Scalar Conformal Blocks
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• Efficient Rules for All Conformal Blocks
• Fake Z
• Ising model close to $d=2$
• Geometric Upper Critical Dimensions of the Ising Model
• Differential operators for superconformal correlation functions
• Fermion-induced quantum critical point in Dirac semimetals: a sign-problem-free quantum Monte Carlo study
• Bootstrapping Mixed MN Correlators in 3D
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
• Bootstrapping Closed Hyperbolic Surfaces
• Platonic Field Theories
• Interacting conformal scalar in a wedge
• Dimensional reduction of higher-point conformal blocks
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• Conformal Properties of Hyperinvariant Tensor Networks
• 3D Ising Model: a view from the Conformal Bootstrap Island
• One-Dimensional Sectors From the Squashed Three-Sphere
• More on Wilson toroidal networks and torus blocks
• Bounding 3d CFT correlators
• Lightcone expansions of conformal blocks in closed form
• On ${\varphi }^3$ Theory Above Six Dimensions
• Conformal partial waves in momentum space
• Complex saddles of three-dimensional de Sitter gravity via holography
• On Conformal Block, Crossing Kernel and Multi-variable Hypergeometric Functions
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• Solving anharmonic oscillator with null states: Hamiltonian bootstrap and Dyson-Schwinger equations
• Bootstrap bound on extremal Reissner-Nordström black hole in AdS
• RepLAB: a computational/numerical approach to representation theory
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Spin-models, dynamics and criticality with atoms in tilted optical superlattices
• Is there supersymmetric Lee-Yang fixed point in three dimensions?
• Renormalization group flows in AdS and the bootstrap program
• Dimensional Reduction by Conformal Bootstrap
• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Exploring Confinement in Anti-de Sitter Space
• The Unique Polyakov Blocks
• Pure anti-de Sitter supergravity and the conformal bootstrap
• Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
• Bootstrap Bounds on Closed Hyperbolic Manifolds
• Playing with the index of M-theory
• Conformality and self-duality of $N_f=2$ QED${}_3$
• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Boundary conformal field theory at the extraordinary transition: The layer susceptibility to $O(\epsilon )$
• Sub-leading conformal dimensions at the O(4) Wilson-Fisher fixed point
• Scale without Conformal Invariance in Dipolar Ferromagnets
• Dark Matter from a Conformal Dark Sector
• Implications of ANEC for SCFTs in four dimensions
• More Analytic Bootstrap: Nonperturbative Effects and Fermions
• Conformal Contact Terms and Semi-Local Terms
• Principle of minimal singularity for Green's functions
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Bootstrapping Lieb-Schultz-Mattis anomalies
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Superfluids, vortices and spinning charged operators in 4d CFT
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Analytic bootstrap for magnetic impurities
• Towards a nonperturbative construction of the $S$-matrix
• Mixed Correlator Dispersive CFT Sum Rules
• Why boundary conditions do not generally determine the universality class for boundary critical behavior
• Universal Spinning Casimir Equations and Their Solutions
• Quantum extraordinary-log universality of boundary critical behavior
• Method of images in defect conformal field theories
• The Inversion Formula and 6j Symbol for 3d Fermions
• Instability of complex CFTs with operators in the principal series
• A CFT Distance Conjecture
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• OPE coefficients in Argyres-Douglas theories
• Bootstrapping the Quantum Hall problem
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• The tricritical Ising CFT and conformal bootstrap
• Positivity, low twist dominance and CSDR for CFTs
• Conformal Fields from Neural Networks
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Twisted bilayer U(1) Dirac spin liquids
• Finite-time scaling beyond the Kibble-Zurek prerequisite in Dirac systems
• Bootstrapping (D, D) Conformal Matter
• The thermal bootstrap for the critical O(N) model
• Conformal Bootstrap Deformations
• Conformal Invariance and Multifractality at Anderson Transitions in Arbitrary Dimensions
• Non-Noetherian conformal scalar fields
• Conformal equations that are not Virasoro or Weyl invariant
• Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit
• Ising string beyond Nambu-Goto
• Deconfined quantum critical point lost in pressurized SrCu2(BO3)2
• Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism
• Freedom near Lightcone and ANEC Saturation
• Quantum Many-body Bootstrap
• Conformal invariance from scale invariance in non-linear sigma models
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Topological terms on topological defects: a quantum Monte Carlo study
• Automorphic Spectra and the Conformal Bootstrap
• Supersymmetric Galilean conformal blocks
• Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions
• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• Semidefinite Programs at Finite Fermion Density
• Further Results on a Function Relevant for Conformal Blocks
• ${\varphi }^n$ trajectory bootstrap
• Hidden orders and phase transitions for the fully packed quantum loop model on the triangular lattice
• Short sighted deep learning
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Emergent ${\mathbb{Z}}_2$ symmetry near a CDW multicritical point
• The ordinary surface universality class of the three-dimensional O($N$) model
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Factorized lightcone expansion of conformal blocks
• Casimir Forces in CFT with Defects and Boundaries
• The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Two- and three-point functions at criticality: Monte Carlo simulations of the three-dimensional $(q+1)$-state clock model
• Scattering length from holographic duality
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• More on Heavy-Light Bootstrap up to Double-Stress-Tensor
• Anomalous Dimensions in Hypercubic Theories
• Conformal perturbation theory confronts lattice results in the vicinity of a critical point
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• Measuring the Boundary Gapless State and Criticality via Disorder Operator
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• QED's in $2+1$ dimensions: complex fixed points and dualities
• Bounds on Triangle Anomalies in (3+1)d
• Bipartite Fluctuations of Critical Fermi Surfaces
• On the consistency of (partially-)massless matter couplings in de Sitter space
• Quantum algorithms for conformal bootstrap
• Topological physics in quantum critical systems
• Bulk-boundary correspondence from hyper-invariant tensor networks
• Ground-state properties via machine learning quantum constraints
• The conformal N-point scalar correlator in coordinate space
• Isomorphisms of 4d N=2 SCFTs from 6d
• Universal scaling in real dimension
• 1d Conformal Field Theory and Dispersion Relations
• Conformal Bootstrap with Reinforcement Learning
• Virasoro blocks and the reparametrization formalism
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity
• On the Conformal Symmetry of Exceptional Scalar Theories
• Nonequilibrium Dynamics of Dirac Quantum Criticality in Imaginary Time
• Comments on Short Multiplets in Superconformal Algebras
• The Parisi-Sourlas Uplift and Infinitely Many Solvable 4d CFTs
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Analytic trajectory bootstrap for matrix models
• Exclusion Inside or at the Border of Conformal Bootstrap Continent
• The gravity dual of Lorentzian OPE blocks
• Disturbing news about the $d=2+\epsilon$ expansion
• 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
• Charging Up the Functional Bootstrap
• Universal Dynamics in Non-Orientable CFT${}_2$
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Regge OPE blocks and light-ray operators
• Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model
• Analytic constraints on the energy-momentum tensor in conformal field theories
• OPE coefficients and the mass-gap from the integrable scattering description of 2D CFT's
• Analyticity and Causality in Conformal Field Theory
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• Conformal Bootstrap Analysis for Localization: Symplectic Case
• Correlators in phase-ordering from Schrödinger-invariance
• Sparsity in the numerical six-point bootstrap
• Spin-Peierls instability of deconfined quantum critical points
• Entanglement entropy of a Rarita-Schwinger field in a sphere
• Conformal invariance and Renormalization Group
• Holographic 2-Point Functions in the Pseudo-Conformal Universe
• Critical Dynamics of the Antiferromagnetic $O(3)$ Nonlinear Sigma Model with Conserved Magnetization
• Lectures on chiral algebras of $\mathcal{N}⩾2$ superconformal field theories
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• A Fuzzy Sphere Journey in Critical Phenomena
• Bootstrapping SU(3) Lattice Yang-Mills Theory
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Non-integrable dimer models: universality and scaling relations
• The Operator Product Expansion in Quantum Field Theory
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance
• Bootstrapping mixed correlators in the 2D Ising model
• Hexagonalization in $Ad{S}_3\times S^3\times T^4$: Mirror Corrections
• Cancellation of IR Divergences in 3d Abelian Gauge Theories
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Bootstrapping Shape Invariance: Numerical Bootstrap as a Detector of Solvable Systems
• How to Succeed at Witten Diagram Recursions without Really Trying
• Cosmology as a CFT${}_1$
• Causality, Crossing and Analyticity in Conformal Field Theories
• Conjecture on the lower bound of the length-scale critical exponent $\nu$ at continuous phase transitions
• Cosmology from Strong Interactions
• On the equivalence of two definitions of conformal primary fields in d > 2 dimensions
• Moments and saddles of heavy CFT correlators
• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models
• Boundary Conformal Field Theory at Large Charge
• Conformal bootstrap in momentum space at finite volume
• Virasoro conformal bootstrap with $c>1$
• Note on surface defects in multiscalar critical models
• Exact 3D Conformal Blocks from Fractional Calculus
• New conformal field theories by gauging electric and magnetic currents
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block
• Higher-form anomalies and state-operator correspondence beyond conformal invariance
• Superconformal blocks for stress-tensor and chiral operators for 4D $\mathcal{N}=2$ superconformal field theories
• Bootstrapping periodic quantum systems
• Boundary critical behavior of the Gross-Neveu-Yukawa model
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• Critical and multicritical Lee-Yang fixed points in the local potential approximation
• Conformal Bootstrap with Duality-Inspired Fusion Rule
• A Monte Carlo approach to the conformal bootstrap
• Conformal anomaly of pseudo-scalar operators
• QFT on Fuzzy AdS Spaces: Classical Limit and Boundary Correlation Functions
• Dynamical kinetic energy quenching in the antiferromagnetic quantum critical metals
• Finite-coupling spectrum of O(N) model in AdS
• Sandpile cascades on oscillator networks: the BTW model meets Kuramoto
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills
• Interplay between reflection positivity and crossing symmetry in the bootstrap approach to CFT
• Non-trivial fixed point of a ${\psi }_d^4$ fermionic theory, II. Anomalous exponent and scaling operators
• Deconfined Quantum Phase Transition of a Higher-Order Symmetry-Protected Topological State
• Two applications of the analytic conformal bootstrap: A quick tour guide
• Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance
• The Cubic Fixed Point at Large $N$
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM
• Analytic Studies of Fermions in the Conformal Bootstrap
• Bootstrapping entanglement in quantum spin systems
• Aspects of 4d supersymmetric dynamics and geometry
• Bootstrap Method in Theoretical Physics
• Bootstrapping Flat-band Superconductors: Rigorous Lower Bounds on Superfluid Stiffness
• Entanglement Complexity in Many-body Systems from Positivity Scaling Laws
• PCT Theorem, Wightman Axioms and Conformal Bootstrap
• Using massless fields for observing black hole features in the collapsed phase of Euclidean dynamical triangulations