Factorized lightcone expansion of conformal blocks

Abstract

We present a factorized decomposition of 4-point scalar conformal blocks near the lightcone, which applies to arbitrary intermediate spin and general spacetime dimensions. Then we discuss the systematic expansion in large intermediate spin and the resummations of the large-spin tails of Regge trajectories. The basic integrals for the Lorentzian inversion are given by Wilson functions.

arXiv comment17 pages; v2: references updated, discussions improved

References in corpus (57)

• A bound on chaos
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• 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
• The Bootstrap Program for Boundary CFT_d
• Conformal Regge theory
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Comments on operators with large spin
• Light-ray operators in conformal field theory
• Large Spin Perturbation Theory
• Averaged Null Energy Condition from Causality
• Universal Constraints on Conformal Operator Dimensions
• More constraining conformal bootstrap
• Bootstrapping the O(N) Archipelago
• A spacetime derivation of the Lorentzian OPE inversion formula
• Carving out OPE space and precise $O(2)$ model critical exponents
• Boundary and Interface CFTs from the Conformal Bootstrap
• A Proof of the Conformal Collider Bounds
• Conformal Field Theories in Fractional Dimensions
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Universal anomalous dimensions at large spin and large twist
• Analytic bootstrap at large spin
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Conformal Bootstrap With Slightly Broken Higher Spin Symmetry
• Conformal Collider Physics from the Lightcone Bootstrap
• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Dimensional Reduction for Conformal Blocks
• The ABC (in any D) of Logarithmic CFT
• Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of $O(N)$ Symmetry with Non-integer $N$
• Simplifying large spin bootstrap in Mellin space
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Bootstrapping the Minimal 3D SCFT
• Anomalous dimensions at finite conformal spin from OPE inversion
• Conformal Blocks in the Large D Limit
• Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT
• Heavy-light Bootstrap from Lorentzian Inversion Formula
• Inverse Bootstrapping Conformal Field Theories
• Conformal bootstrap for percolation and polymers
• Conformal Bootstrap Analysis for Yang-Lee Edge Singularity
• Resummation at finite conformal spin
• Crossing symmetry and Higher spin towers
• Conformal Bootstrap Analysis for Single and Branched Polymers
• Dimensional Reduction by Conformal Bootstrap
• The Inversion Formula and 6j Symbol for 3d Fermions

Cited by in corpus (7)

• Helicity basis for three-dimensional conformal field theory
• Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
• Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising Model
• Ising model close to $d=2$
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories