A tauberian theorem for the conformal bootstrap

Abstract

For expansions in one-dimensional conformal blocks, we provide a rigorous link between the asymptotics of the spectral density of exchanged primaries and the leading singularity in the crossed channel. Our result has a direct application to systems of SL(2,R)-invariant correlators (also known as 1d CFTs). It also puts on solid ground a part of the lightcone bootstrap analysis of the spectrum of operators of high spin and bounded twist in CFTs in d>2. In addition, a similar argument controls the spectral density asymptotics in large N gauge theories.

36pp; v2: refs and comments added, misprints corrected

References in corpus (38)

• Comments on the Sachdev-Ye-Kitaev model
• Bounding scalar operator dimensions in 4D CFT
• Solving the 3D Ising Model with the Conformal Bootstrap
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• 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
• The Analytic Bootstrap and AdS Superhorizon Locality
• Analyticity in Spin in Conformal Theories
• Convexity and Liberation at Large Spin
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• 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
• OPE Convergence in Conformal Field Theory
• The S-matrix Bootstrap I: QFT in AdS
• Bootstrapping the 3d Ising twist defect
• Conformal Partial Waves: Further Mathematical Results
• Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Defects in conformal field theory
• Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Conformal Invariance in the Long-Range Ising Model
• Universal anomalous dimensions at large spin and large twist
• Long-range critical exponents near the short-range crossover
• Analytic bootstrap at large spin
• Conformal Bootstrap With Slightly Broken Higher Spin Symmetry
• Crossing Symmetry in Alpha Space
• Conformal Collider Physics from the Lightcone Bootstrap
• Remarks on the Convergence Properties of the Conformal Block Expansion
• Large spin systematics in CFT
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• Cut-touching linear functionals in the conformal bootstrap
• Static hole in a critical antiferromagnet: field-theoretic renormalization group
• Glueball and meson propagators of any spin in large-N QCD
• Extremal bootstrapping: go with the flow

Cited by in corpus (61)

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• The Analytic Functional Bootstrap II: Natural Bases for the Crossing Equation
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• Dispersive CFT Sum Rules
• Universal Dynamics of Heavy Operators in CFT${}_2$
• Universality at large transverse spin in defect CFT
• The critical O(N) CFT: Methods and conformal data
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• Thermal Order in Conformal Theories
• Analytic Euclidean Bootstrap
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• Simplifying large spin bootstrap in Mellin space
• Tauberian-Cardy formula with spin
• Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
• Analytic Functional Bootstrap for CFTs in $d>1$
• A Crossing-Symmetric OPE Inversion Formula
• Non-Gaussianities in the Statistical Distribution of Heavy OPE Coefficients and Wormholes
• Gravitational Regge bounds
• Beurling-Selberg Extremization and Modular Bootstrap at High Energies
• Modular crossings, OPE coefficients and black holes
• OPE statistics from higher-point crossing
• On the Positive Geometry of Conformal Field Theory
• Distributions in CFT II. Minkowski Space
• High-dimensional sphere packing and the modular bootstrap
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• A Basis of Analytic Functionals for CFTs in General Dimension
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
• Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
• Universality in asymptotic bounds and its saturation in $2$D CFT
• Multiboundary wormholes and OPE statistics
• Conformal Quantum Mechanics and Sine-Square Deformation
• 2d Galilean Field Theories with Anisotropic Scaling
• On Galilean conformal bootstrap
• EFT Asymptotics: the Growth of Operator Degeneracy
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Scalar Blocks as Gravitational Wilson Networks
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Bound on asymptotics of magnitude of three point coefficients in 2D CFT
• Dispersive Sum Rules in AdS${}_2$
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Higher-Dimensional Symmetry of AdS${}_2\times$S${}^2$ Correlators
• Lightcone expansions of conformal blocks in closed form
• Renormalization group flows in AdS and the bootstrap program
• Hartle-Hawking state and its factorization in 3d gravity
• Unitarity and Universality in non relativistic Conformal Field theory
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• The Inversion Formula and 6j Symbol for 3d Fermions
• Lightcone Modular Bootstrap and Tauberian Theory: A Cardy-like Formula for Near-extremal Black Holes
• Polyakov blocks for the 1D CFT mixed correlator bootstrap
• Conformal line defects at finite temperature
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Theorems for the Lightcone Bootstrap
• Universal Dynamics in Non-Orientable CFT${}_2$
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Moments and saddles of heavy CFT correlators
• Nonperturbative dynamics of (2+1)d ${\varphi }^4$-theory from Hamiltonian truncation
• Analytic Studies of Fermions in the Conformal Bootstrap