Light-ray operators in conformal field theory

Abstract

We argue that every CFT contains light-ray operators labeled by a continuous spin J. When J is a positive integer, light-ray operators become integrals of local operators over a null line. However for non-integer J, light-ray operators are genuinely nonlocal and give the analytic continuation of CFT data in spin described by Caron-Huot. A key role in our construction is played by a novel set of intrinsically Lorentzian integral transforms that generalize the shadow transform. Matrix elements of light-ray operators can be computed via the integral of a double-commutator against a conformal block. This gives a simple derivation of Caron-Huot's Lorentzian OPE inversion formula and lets us generalize it to arbitrary four-point functions. Furthermore, we show that light-ray operators enter the Regge limit of CFT correlators, and generalize conformal Regge theory to arbitrary four-point functions. The average null energy operator is an important example of a light-ray operator. Using our construction, we find a new proof of the average null energy condition (ANEC), and furthermore generalize the ANEC to continuous spin.

arXiv comment74 pages plus appendices; v2: fixed typos, updated references, expanded discussion of even spin/odd spin trajectories; v3: fixed some factors of 2

References in corpus (71)

• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Conformal collider physics: Energy and charge correlations
• Conformal Four Point Functions and the Operator Product Expansion
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• The Pomeron and Gauge/String Duality
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• Two-dimensional conformal field theory and the butterfly effect
• Convexity and Liberation at Large Spin
• Projectors, Shadows, and Conformal Blocks
• The Uses of Conformal Symmetry in QCD
• Bootstrapping the O(N) Vector Models
• Conformal Regge theory
• A Quantum Focussing Conjecture
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Spinning Conformal Blocks
• Bootstrapping Mixed Correlators in the 3D Ising Model
• OPE Convergence in Conformal Field Theory
• Large Spin Perturbation Theory
• Averaged Null Energy Condition from Causality
• Causality Constraints in Conformal Field Theory
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Unitarity and the Holographic S-Matrix
• Proof of the Quantum Null Energy Condition
• A Stereoscopic Look into the Bulk
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• More on Supersymmetric and 2d Analogs of the SYK Model
• A spacetime derivation of the Lorentzian OPE inversion formula
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• Eikonal Approximation in AdS/CFT: From Shock Waves to Four-Point Functions
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• A Proof of the Conformal Collider Bounds
• Markov property of the CFT vacuum and the a-theorem
• Weight Shifting Operators and Conformal Blocks
• Modular Hamiltonians on the null plane and the Markov property of the vacuum state
• The Conformal Bootstrap at Finite Temperature
• Deep Inelastic Scattering in Conformal QCD
• Bounds for OPE coefficients on the Regge trajectory
• Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling
• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• Superintegrability of $d$-dimensional Conformal Blocks
• Conformal Bootstrap With Slightly Broken Higher Spin Symmetry
• Universality at large transverse spin in defect CFT
• Conformal Collider Physics from the Lightcone Bootstrap
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Holographic Reconstruction of AdS Exchanges from Crossing Symmetry
• Eikonalization of Conformal Blocks
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• Simplifying large spin bootstrap in Mellin space
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• Non-Abelian Binding Energies from the Lightcone Bootstrap
• Conformal Field Theories and Deep Inelastic Scattering
• Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Universal Bounds on Operator Dimensions from the Average Null Energy Condition
• BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin
• Three-point correlator of twist-2 operators in BFKL limit
• Graviton Scattering and a Sum Rule for the c Anomaly in 4D CFT
• Wedge reflection positivity
• Perturbative Four-Point Functions from the Analytic Conformal Bootstrap
• Minkowski Conformal Blocks and the Regge Limit for SYK-like Models
• The Regge Limit for Green Functions in Conformal Field Theory
• The Analytic Bootstrap in Fermionic CFTs

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