Eikonalization of Conformal Blocks

Abstract

Classical field configurations such as the Coulomb potential and Schwarzschild solution are built from the t-channel exchange of many light degrees of freedom. We study the CFT analog of this phenomenon, which we term the `eikonalization' of conformal blocks. We show that when an operator $T$ appears in the OPE $\mathcal{O}(x)\mathcal{O}(0)$, then the large spin $\ell$ Fock space states $[TT\cdots T{]}_{\ell }$ also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an $⟨\mathcal{OOOO}⟩$ correlator build the classical `$T$ field' in the dual AdS description. In some limits the sum of all Fock space exchanges can be represented as the exponential of a single $T$ exchange in the 4-pt correlator of $\mathcal{O}$. Our results should be useful for systematizing $1/\ell$ perturbation theory in general CFTs and simplifying the computation of large spin OPE coefficients. As examples we obtain the leading $\log \ell$ dependence of Fock space conformal block coefficients, and we directly compute the OPE coefficients of the simplest `triple-trace' operators.

32+17 pages, 6 figures; references added, discussion of eikonal limit clarified

References in corpus (29)

• Holography from Conformal Field Theory
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Writing CFT correlation functions as AdS scattering amplitudes
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• Comments on operators with large spin
• The $(2,0)$ superconformal bootstrap
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• 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
• Universal anomalous dimensions at large spin and large twist
• Conformal Bootstrap, Universality and Gravitational Scattering
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Bootstrapping SCFTs with Four Supercharges
• Virasoro conformal blocks in closed form
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange
• A Semidefinite Program Solver for the Conformal Bootstrap
• D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models
• JuliBootS: a hands-on guide to the conformal bootstrap
• High Energy Scattering in the AdS/CFT Correspondence
• IR Renormalons vs. Operator Product Expansion in Supersymmetric and Related Gauge Theories
• Resurgence, Operator Product Expansion, and Remarks on Renormalons in Supersymmetric Yang-Mills
• Lessons from crossing symmetry at large N

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• A Proof of the Conformal Collider Bounds
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• The Conformal Bootstrap at Finite Temperature
• Bootstrapping $\mathcal{N}=2$ chiral correlators
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• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
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• Unitarity Methods in AdS/CFT
• Dimensional Reduction for Conformal Blocks
• A New Spin on Causality Constraints
• Universality of Sparse $d>2$ Conformal Field Theory at Large $N$
• Simplifying large spin bootstrap in Mellin space
• Non-Abelian Binding Energies from the Lightcone Bootstrap
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• Black Holes, Heavy States, Phase Shift and Anomalous Dimensions
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Universality of Quantum Information in Chaotic CFTs
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Scalar CFTs and Their Large N Limits
• Subleading Eikonal, AdS/CFT and Double Stress Tensors
• Bootstrapping the 3d Ising Stress Tensor
• Universal Asymptotics for High Energy CFT Data
• On the Virasoro six-point identity block and chaos
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• Regenesis and quantum traversable wormholes
• Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
• Six-point functions and collisions in the black hole interior
• Model-Dependence of Minimal-Twist OPEs in $d>2$ Holographic CFTs
• Generalizing event shapes: In search of lost collider time
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Minkowski Conformal Blocks and the Regge Limit for SYK-like Models
• A view of the bulk from the worldline
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• Virasoro blocks at large exchange dimension
• Ergodicity breaking and deviation from Eigenstate Thermalisation in relativistic QFT
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Reparametrization mode Ward Identities and chaos in higher-pt. correlators in CFT${}_2$
• Universal thermalization dynamics in (1+1)d QFTs
• Flat-space Quantum Gravity in AdS/CFT
• Analytic Studies of Fermions in the Conformal Bootstrap