The Bootstrap Program for Boundary CFT_d

Abstract

We study the constraints of crossing symmetry and unitarity for conformal field theories in the presence of a boundary, with a focus on the Ising model in various dimensions. We show that an analytic approach to the bootstrap is feasible for free-field theory and at one loop in the epsilon expansion, but more generally one has to resort to numerical methods. Using the recently developed linear programming techniques we find several interesting bounds for operator dimensions and OPE coefficients and comment on their physical relevance. We also show that the "boundary bootstrap" can be easily applied to correlation functions of tensorial operators and study the stress tensor as an example. In the appendices we present conformal block decompositions of a variety of physically interesting correlation functions.

60 pages, 12 figures. v2: minor update to conclusions, added references

References in corpus (4)

• Bounds on 4D Conformal and Superconformal Field Theories
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Central Charge Bounds in 4D Conformal Field Theory
• Lower bound on the entropy of boundaries and junctions in 1+1d quantum critical systems

Cited by in corpus (225)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• The Analytic Bootstrap and AdS Superhorizon Locality
• Convexity and Liberation at Large Spin
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Bootstrapping the O(N) Vector Models
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• Radial Coordinates for Conformal Blocks
• The $(2,0)$ superconformal bootstrap
• Bootstrapping the 3d Ising twist defect
• Bootstrapping the O(N) Archipelago
• Carving out OPE space and precise $O(2)$ model critical exponents
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Boundary and Interface CFTs from the Conformal Bootstrap
• Conformal Field Theories in Fractional Dimensions
• Boundary Conformal Field Theory and a Boundary Central Charge
• Gapless topological phases and symmetry-enriched quantum criticality
• The $\mathcal{N}=2$ superconformal bootstrap
• Weight Shifting Operators and Conformal Blocks
• Defects in conformal field theory
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• From correlation functions to event shapes
• BCFT entanglement entropy at large central charge and the black hole interior
• Conformal Invariance in the Long-Range Ising Model
• A General Proof of the Quantum Null Energy Condition
• Recursion Relations for Conformal Blocks
• The Conformal Bootstrap at Finite Temperature
• Bootstrapping the half-BPS line defect
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• The Analytic Functional Bootstrap I: 1D CFTs and 2D S-Matrices
• On Scale and Conformal Invariance in Four Dimensions
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Diagonal Limit for Conformal Blocks in d Dimensions
• Towards a $C$-theorem in defect CFT
• Renormalization Group Flows on Line Defects
• The 3d Stress-Tensor Bootstrap
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
• Universality at large transverse spin in defect CFT
• 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
• Localized magnetic field in the $O(N)$ model
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• The critical O(N) CFT: Methods and conformal data
• Covariant Approaches to Superconformal Blocks
• More $\mathcal{N}=4$ superconformal bootstrap
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Eikonalization of Conformal Blocks
• Line and surface defects for the free scalar field
• Radial expansion for spinning conformal blocks
• Solving M-theory with the Conformal Bootstrap
• The Mellin Formalism for Boundary CFT${}_d$
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• An Analytic Approach to BCFT${}_d$
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• Analytic Bootstrap for Boundary CFT
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Line defects and radiation in $\mathcal{N}=2$ theories
• Harmony of Spinning Conformal Blocks
• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• Exact Virasoro Blocks from Wilson Lines and Background-Independent Operators
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• CFT in AdS and boundary RG flows
• Bootstrapping critical Ising model on three-dimensional real projective space
• Superconformal surfaces in four dimensions
• A Semidefinite Program Solver for the Conformal Bootstrap
• Spinning operators and defects in conformal field theory
• Casimir recursion relations for general conformal blocks
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
• From Spinning Conformal Blocks to Matrix Calogero-Sutherland Models
• An Exact Operator That Knows Its Location
• Holo-ween
• 3d Abelian Gauge Theories at the Boundary
• Non-Abelian Binding Energies from the Lightcone Bootstrap
• Bootstrapping boundary-localized interactions
• Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
• On Conformal Field Theories With Extremal a/c Values
• Bounds on OPE Coefficients in 4D Conformal Field Theories
• A Quantum Check of AdS/dCFT
• Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations
• Radial coordinates for defect CFTs
• Universal Asymptotics for High Energy CFT Data
• $O(N)$ Models with Boundary Interactions and their Long Range Generalizations
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• Calogero-Sutherland Approach to Defect Blocks
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Fermion-Scalar Conformal Blocks
• Notes on a Surface Defect in the $O(N)$ Model
• Conformal Blocks in the Large D Limit
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory
• Three-point energy correlators and the celestial block expansion
• Fermions in AdS and Gross-Neveu BCFT
• Probing beyond ETH at large $c$
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• Structure of Holographic BCFT Correlators from Geodesics
• Spinning conformal defects
• Looking for (and not finding) a bulk brane
• Monodromy Defects in Free Field Theories
• Crossing Kernels for Boundary and Crosscap CFTs
• Analytic bootstrap for the localized magnetic field
• On Marginal Operators in Boundary Conformal Field Theory
• Aspects of CFTs on Real Projective Space
• Operator expansions, layer susceptibility and two-point functions in BCFT
• On Analytic Bootstrap for Interface and Boundary CFT
• 't Hooft anomalies and boundaries
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• 3d Abelian Dualities with Boundaries
• A dispersion relation for defect CFT
• Coupled minimal models revisited
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• One-point functions in AdS/dCFT
• Free energy and defect $C$-theorem in free scalar theory
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Inverse Bootstrapping Conformal Field Theories
• Bootstrapping the 3d Ising model at finite temperature
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• New Methods for Conformal Correlation Functions
• Critical Ising Model in Varying Dimension by Conformal Bootstrap
• Superconformal Models for Graphene and Boundary Central Charges
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• The unitary subsector of generalized minimal models
• Operator product expansion for conformal defects
• Conformal dispersion relations for defects and boundaries
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• Composite operators near the boundary
• Comments on Defining Entanglement Entropy
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• Conformal Manifolds with Boundaries or Defects
• New method for the conformal bootstrap with OPE truncations
• Conformal symmetry of the critical 3D Ising model inside a sphere
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Gravitational dual of the Rényi twist displacement operator
• The Shadow Formalism of Galilean CFT${}_2$
• Conformal Bootstrap near the edge
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Correlators of Mixed Symmetry Operators in Defect CFTs
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Three ways to solve critical ${\varphi }^4$ theory on $4-\epsilon$ dimensional real projective space: perturbation, bootstrap, and Schwinger-Dyson equation
• Ising model close to $d=2$
• Anomalous dimensions of spinning operators from conformal symmetry
• Boundary Kinematic Space
• Holographic two-point functions for Janus interfaces in the $D1/D5$ CFT
• The Epsilon-Expansion from Conformal Field Theory
• Interacting conformal scalar in a wedge
• Analytic and numerical bootstrap for the long-range Ising model
• Double Trace Interfaces
• Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet
• Observations on BPS observables in 6d
• Renormalization group flows in AdS and the bootstrap program
• OPE Coefficients of the 3D Ising model with a trapping potential
• Exploring Confinement in Anti-de Sitter Space
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• Boundary conformal field theory at the extraordinary transition: The layer susceptibility to $O(\epsilon )$
• An Effective Theory for Holographic RG Flows
• Defect Conformal Blocks from Appell Functions
• On actions for (entangling) surfaces and DCFTs
• Analytic bootstrap for magnetic impurities
• A Sum Rule for Boundary Contributions to the Trace Anomaly
• Unitarity violation in non-integer dimensional Gross-Neveu-Yukawa model
• Twisted holography of defect fusions
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Universal Bounds on Operator Dimensions in General 2D Conformal Field Theories
• (No) Bootstrap for the Fractal Ising Model
• Method of images in defect conformal field theories
• Universal Spinning Casimir Equations and Their Solutions
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Why boundary conditions do not generally determine the universality class for boundary critical behavior
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory
• Holographic correlators of semiclassical states in defect CFTs
• Positivity, low twist dominance and CSDR for CFTs
• On co-dimension two defect operators
• Boundary Holographic Witten Diagrams
• The Functional Bootstrap for Boundary CFT
• Conformal blocks for highly disparate scaling dimensions
• The ordinary surface universality class of the three-dimensional O($N$) model
• Casimir Forces in CFT with Defects and Boundaries
• Conformal line defects at finite temperature
• Factorized lightcone expansion of conformal blocks
• Ironing out the crease
• Boundary operator expansion and extraordinary phase transition in the tricritical O(N) model
• B-type anomaly coefficients for the D3-D5 domain wall
• Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap
• On the EFT of Conformal Symmetry Breaking
• More on Boundary Holographic Witten Diagrams
• Deconstructing Conformal Blocks in 4D CFT
• Spontaneous symmetry breaking in free theories with boundary potentials
• Exclusion Inside or at the Border of Conformal Bootstrap Continent
• Probing Defects with Quantum Simulator Snapshots
• Boundary criticality for the Gross-Neveu-Yukawa models
• Holographic 2-Point Functions in the Pseudo-Conformal Universe
• Boundary phase transitions of two-dimensional quantum critical XXZ model
• Surface Operators in Superspace
• From $\mathcal{N}=4$ Super-Yang-Mills on ${\mathbb{RP}}^4$ to bosonic Yang-Mills on ${\mathbb{RP}}^2$
• Line defects in the 3d Ising model
• CFTs on curved spaces
• Surface critical behavior of the three-dimensional O(3) model
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Disclinations, dislocations, and emanant flux at Dirac criticality
• How to Succeed at Witten Diagram Recursions without Really Trying
• One-point functions for doubly-holographic BCFTs and backreacting defects
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block
• Boundary Conformal Field Theory at Large Charge
• B-type anomaly coefficients for the D3-D7 domain wall
• A Monte Carlo approach to the conformal bootstrap
• Fusion of spin fields in $W_3$ conformal field theories
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Analytic Studies of Fermions in the Conformal Bootstrap
• Boundary criticality in two-dimensional interacting topological insulators
• Conformal Bootstrap with Duality-Inspired Fusion Rule
• Finite-coupling spectrum of O(N) model in AdS
• Boundary conformal field theory, holography and bulk locality
• Three-dimensional quantum gravity according to ST modular bootstrap