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Title: Eikonalization of conformal blocks

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.
 [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)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 1029-8479; PII: 2021; TRN: US1500807
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 9; Journal ID: ISSN 1029-8479
Springer Berlin
Research Org:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS AdS-CFT correspondence; conformal and W symmetry