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Eikonalization of conformal blocks

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [2]
  1. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Johns Hopkins Univ., Baltimore, MD (United States)
  3. Boston Univ., Boston, MA (United States)
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 Ο(x)Ο(0), then the large spin Fock space states [TT···T] also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an 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 O. Our results should be useful for systematizing 1/ℓ perturbation theory in general CFTs and simplifying the computation of large spin OPE coefficients. As examples we obtain the leading log ℓ dependence of Fock space conformal block coefficients, and we directly compute the OPE coefficients of the simplest ‘triple-trace’ operators.
Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC03-76SF00515
OSTI ID:
1225807
Report Number(s):
SLAC-PUB--16685; PII: 2021
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 9 Vol. 2015; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (28)

Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators journal January 2016
Universality of sparse d > 2 conformal field theory at large N journal March 2017
The lightcone bootstrap and the spectrum of the 3d Ising CFT journal March 2017
Universality of quantum information in chaotic CFTs journal March 2018
An algebraic approach to the analytic bootstrap journal April 2017
Hawking from Catalan journal May 2016
Causality constraints in conformal field theory journal May 2016
A Mellin space approach to the conformal bootstrap journal May 2017
Black hole collapse in the 1/c expansion journal July 2016
Dimensional reduction for conformal blocks journal September 2016
Scalar CFTs and their large N limits journal September 2018
A new spin on causality constraints journal October 2016
The conformal bootstrap at finite temperature journal October 2018
Regenesis and quantum traversable wormholes journal October 2019
Bootstrapping the O(N) archipelago journal November 2015
Virasoro conformal blocks and thermality from classical background fields journal November 2015
Light-ray operators in conformal field theory journal November 2018
Eigenstate thermalization hypothesis in conformal field theory journal March 2018
The (2, 0) superconformal bootstrap journal January 2016
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text January 2017
Virasoro Conformal Blocks and Thermality from Classical Background Fields text January 2015
Causality Constraints in Conformal Field Theory text January 2015
Hawking from Catalan text January 2015
Eigenstate Thermalization Hypothesis in Conformal Field Theory text January 2016
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text January 2017
Scalar CFTs and Their Large N Limits text January 2017
The Conformal Bootstrap at Finite Temperature text January 2018
Light-ray operators in conformal field theory text January 2018

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