Eikonalization of conformal blocks

Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.; Wang, Junpu

doi:10.1007/JHEP09(2015)019

Title: Eikonalization of conformal blocks

Journal Article · Thu Sep 03 00:00:00 EDT 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP09(2015)019· OSTI ID:1225807

Fitzpatrick, A. Liam ^[1]; Kaplan, Jared ^[2]; Walters, Matthew T. ^[3]; Wang, Junpu ^[2]

Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Johns Hopkins Univ., Baltimore, MD (United States)
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]_ℓ 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.

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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; TRN: US1500807

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 46 works

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