Bootstrapping the O(N) Vector Models

Abstract

We study the conformal bootstrap for 3D CFTs with O(N) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N) singlet and symmetric tensor operators appearing in the ${\varphi }_i\times {\varphi }_j$ OPE, where ${\varphi }_i$ is a fundamental of O(N). Comparing these bounds to previous determinations of critical exponents in the O(N) vector models, we find strong numerical evidence that the O(N) vector models saturate the bootstrap constraints at all values of N. We also compute general lower bounds on the central charge, giving numerical predictions for the values realized in the O(N) vector models. We compare our predictions to previous computations in the 1/N expansion, finding precise agreement at large values of N.

26 pages, 5 figures; V2: typos corrected

References in corpus (12)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Writing CFT correlation functions as AdS scattering amplitudes
• Bounds on 4D Conformal and Superconformal Field Theories
• The critical exponents of the superfluid transition in He4
• The $(2,0)$ superconformal bootstrap
• Comments on Unparticles
• Bounds in 4D Conformal Field Theories with Global Symmetry
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Central Charge Bounds in 4D Conformal Field Theory
• D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models
• Conformal Blocks in the Large D Limit
• The critical equation of state of the three-dimensional O(N) universality class: N>4

Cited by in corpus (240)

• Quantum entanglement in condensed matter systems
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• Analyticity in Spin in Conformal Theories
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Deconfined quantum critical points: symmetries and dualities
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Light-ray operators in conformal field theory
• Witten Diagrams Revisited: The AdS Geometry of Conformal Blocks
• The $(2,0)$ superconformal bootstrap
• Bootstrapping the 3d Ising twist defect
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Bootstrapping the O(N) Archipelago
• Universality of corner entanglement in conformal field theories
• Carving out OPE space and precise $O(2)$ model critical exponents
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• A Proof of the Conformal Collider Bounds
• Conformal Field Theories in Fractional Dimensions
• A Cheap Alternative to the Lattice?
• The $\mathcal{N}=2$ superconformal bootstrap
• Bootstrapping 3D Fermions
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Recursion Relations for Conformal Blocks
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Duality between $(2+1)d$ Quantum Critical Points
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Conformal Bootstrap Dashing Hopes of Emergent Symmetry
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Multipoint Conformal Blocks in the Comb Channel
• The 3d Stress-Tensor Bootstrap
• Bootstrapping 3D Fermions with Global Symmetries
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
• Weak Gravity Conjecture in AdS/CFT
• Corner contributions to holographic entanglement entropy
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Loop Equations and bootstrap methods in the lattice
• 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
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• The critical O(N) CFT: Methods and conformal data
• Covariant Approaches to Superconformal Blocks
• Anomalous dimensions in CFT with weakly broken higher spin symmetry
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Eikonalization of Conformal Blocks
• Towards Bootstrapping QED${}_3$
• The Random-Bond Ising Model in 2.01 and 3 Dimensions
• Radial expansion for spinning conformal blocks
• Solving M-theory with the Conformal Bootstrap
• The $O(N)$ Model in $4<d<6$: Instantons and Complex CFTs
• Momentum space approach to crossing symmetric CFT correlators
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• Mellin space bootstrap for global symmetry
• Seed Conformal Blocks in 4D CFT
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Critical exponents of O(N) models in fractional dimensions
• PyCFTBoot: A flexible interface for the conformal bootstrap
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• Bootstrapping the long-range Ising model in three dimensions
• Free box^k Scalar Conformal Field Theory
• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• Generalized $F$-Theorem and the $\epsilon$ Expansion
• The S-matrix Bootstrap IV: Multiple Amplitudes
• Bootstrapping critical Ising model on three-dimensional real projective space
• Dimensional Reduction for Conformal Blocks
• Momentum-space conformal blocks on the light cone
• A Semidefinite Program Solver for the Conformal Bootstrap
• The Gross-Neveu-Yukawa Archipelago
• The ABC (in any D) of Logarithmic CFT
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• Spinning operators and defects in conformal field theory
• Casimir recursion relations for general conformal blocks
• Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Decoding a Three-Dimensional Conformal Manifold
• Generalized bootstrap equations for N=4 SCFT
• Scalar-Vector Bootstrap
• Non-Abelian Binding Energies from the Lightcone Bootstrap
• (2,2) Superconformal Bootstrap in Two Dimensions
• JuliBootS: a hands-on guide to the conformal bootstrap
• Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
• On the four-point function of the stress-energy tensors in a CFT
• Notes on flat-space limit of AdS/CFT
• Analytic Functional Bootstrap for CFTs in $d>1$
• Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator
• Accidental Symmetries and the Conformal Bootstrap
• Bounds on OPE Coefficients in 4D Conformal Field Theories
• Scalar CFTs and Their Large N Limits
• Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs
• Radial coordinates for defect CFTs
• From Gaudin Integrable Models to $d$-dimensional Multipoint Conformal Blocks
• Universal Asymptotics for High Energy CFT Data
• Bounds on corner entanglement in quantum critical states
• Bootstrapping the 3d Ising Stress Tensor
• Bootstrapping the Minimal 3D SCFT
• Scale invariance implies conformal invariance for the three-dimensional Ising model
• Recursion relation for general 3d blocks
• New Developments in the Numerical Conformal Bootstrap
• Higher-Point Conformal Blocks in the Comb Channel
• $\epsilon$-Expansion in Critical ${\varphi }^3$-Theory on Real Projective Space from Conformal Field Theory
• On $C_J$ and $C_T$ in the Gross-Neveu and $O(N)$ Models
• Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ
• 3D CFT Archipelago from Single Correlator Bootstrap
• Distributions in CFT II. Minkowski Space
• Universal corner entanglement of Dirac fermions and gapless bosons from the continuum to the lattice
• Fermion-Scalar Conformal Blocks
• Six dimensional QCD at two loops
• Three-point energy correlators and the celestial block expansion
• Bootstrapping hypercubic and hypertetrahedral theories in three dimensions
• Conformal manifolds: ODEs from OPEs
• Searching for gauge theories with the conformal bootstrap
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories II
• Critical O(N) model to order ${\epsilon }^4$ from analytic bootstrap
• Large $N_f$ quantum field theory
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Thermal Conformal Blocks
• More on analytic bootstrap for O(N) models
• A multipoint conformal block chain in $d$ dimensions
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Recursion relations for 5-point conformal blocks
• Scaling the semidefinite program solver SDPB
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT
• Looking for a bulk point
• Bootstrap experiments on higher dimensional CFTs
• N=4 Superconformal Bootstrap of the K3 CFT
• Exploring the Minimal 4D $\mathcal{N}=1$ SCFT
• Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs
• Distributions in CFT I. Cross-Ratio Space
• Towards Bootstrapping RG flows: Sine-Gordon in AdS
• Mixed Scalar-Current bootstrap in three dimensions
• AdS${}_4$/CFT${}_3$ for Unprotected Operators
• Bootstrapping MN and Tetragonal CFTs in Three Dimensions
• Bound states of the ${\varphi }^4$ model via the nonperturbative renormalization group
• Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
• Inverse Bootstrapping Conformal Field Theories
• New Methods for Conformal Correlation Functions
• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• Conformal bootstrap for percolation and polymers
• Critical Ising Model in Varying Dimension by Conformal Bootstrap
• A Note on Inhomogeneous Ground States at Large Global Charge
• Constraining quantum critical dynamics: 2+1D Ising model and beyond
• Bootstrapping the $\cN=1$ SCFT in three dimensions
• Towards Feynman rules for conformal blocks
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• Spectrum of the Wilson-Fisher conformal field theory on the torus
• Observables in Inhomogeneous Ground States at Large Global Charge
• Non-gaussianity of the critical 3d Ising model
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Bootstrapping traceless symmetric $O(N)$ scalars
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Comments on Determinant Formulas for General CFTs
• Charting the space of 3D CFTs with a continuous global symmetry
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• blocks_3d: Software for general 3d conformal blocks
• New method for the conformal bootstrap with OPE truncations
• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap
• Holography of Information in AdS/CFT
• Bootstrapping $O(N)$ Vector Models with Four Supercharges in $3\le d\le 4$
• Closed-form expression for cross-channel conformal blocks near the lightcone
• Critical properties of the Néel/algebraic-spin-liquid transition
• Precise Critical Exponents of the O(N)-Symmetric Quantum field Model using Hypergeometric-Meijer Resummation
• Exploring $SU(N)$ adjoint correlators in $3d$
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• Tripartite information at long distances
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• Conformal Bootstrap Signatures of the Tricritical Ising Universality Class
• Regge trajectories for the (2,0) theories
• Conformal Regge Theory at Finite Boost
• The Epsilon-Expansion from Conformal Field Theory
• Conformal invariance and vector operators in the $O(N)$ model
• Conformal partial waves in momentum space
• Lightcone expansions of conformal blocks in closed form
• 2d small N=4 Long-multiplet superconformal block
• Collusion of Interactions and Disorder at the Superfluid-Insulator Transition: A Dirty 2d Quantum Critical Point
• An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena
• Bootstrap bound on extremal Reissner-Nordström black hole in AdS
• A Holographic Model for Quantum Critical Responses
• OPE Coefficients of the 3D Ising model with a trapping potential
• Conformality and self-duality of $N_f=2$ QED${}_3$
• Pure anti-de Sitter supergravity and the conformal bootstrap
• Conformal bounds in three dimensions from entanglement entropy
• Scale without Conformal Invariance in Dipolar Ferromagnets
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Mixed Correlator Dispersive CFT Sum Rules
• More Analytic Bootstrap: Nonperturbative Effects and Fermions
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation
• Unitarity violation in non-integer dimensional Gross-Neveu-Yukawa model
• (No) Bootstrap for the Fractal Ising Model
• OPE coefficients in Argyres-Douglas theories
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Universal Bounds on Operator Dimensions in General 2D Conformal Field Theories
• The tricritical Ising CFT and conformal bootstrap
• Conformal Bootstrap Deformations
• Recursion Relations in $p$-adic Mellin Space
• Bootstrapping (D, D) Conformal Matter
• Partition Functions with spin in AdS_2 via Quasinormal Mode Methods
• Conformal Fields from Neural Networks
• Evidence for 3d bosonization from monopole operators
• Six dimensional Landau-Ginzburg-Wilson theory
• Bootstrapping Pure Quantum Gravity in AdS3
• Automorphic Spectra and the Conformal Bootstrap
• Conformal blocks for highly disparate scaling dimensions
• Determinant Formula for Parabolic Verma Modules of Lie Superalgebras
• Interpolating between $a$ and $F$
• Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions
• An Algebraic Approach to the Analytic Bootstrap
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Non-compact lattice Higgs model with Abelian discrete gauge groups: phase diagram and gauge symmetry enlargement
• Quantum Groups as Global Symmetries
• Counting Conformal Correlators
• General Bootstrap Equations in 4D CFTs
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity
• Comments on Short Multiplets in Superconformal Algebras
• The Parisi-Sourlas Uplift and Infinitely Many Solvable 4d CFTs
• autoboot: A generator of bootstrap equations with global symmetry
• Charging Up the Functional Bootstrap
• Exclusion Inside or at the Border of Conformal Bootstrap Continent
• Higgs Phases and Boundary Criticality
• Sparsity in the numerical six-point bootstrap
• $F_4$ symmetric ${\varphi }^3$ theory at four loops
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Moments and saddles of heavy CFT correlators
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block
• Critical Exponents of the O(N)-symmetric ${\varphi }^4$ Model from the \boldmath{\large{ ${\epsilon }^7$}} Hypergeometric-Meijer Resummation
• Note on surface defects in multiscalar critical models
• Conformal bootstrap in momentum space at finite volume
• A Monte Carlo approach to the conformal bootstrap
• Analytic Studies of Fermions in the Conformal Bootstrap
• Conformal Bootstrap with Duality-Inspired Fusion Rule
• Fusion of spin fields in $W_3$ conformal field theories
• Conformal amplitude hierarchy and the Poincare disk
• Multi-fixed point numerical conformal bootstrap: a case study with structured global symmetry