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Title: 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 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.

Authors:
 [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:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1225807
Report Number(s):
SLAC-PUB-16685
Journal ID: ISSN 1029-8479; PII: 2021; TRN: US1500807
Grant/Contract Number:  
AC03-76SF00515
Resource Type:
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
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT correspondence; conformal and W symmetry

Citation Formats

Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T., and Wang, Junpu. Eikonalization of conformal blocks. United States: N. p., 2015. Web. doi:10.1007/JHEP09(2015)019.
Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T., & Wang, Junpu. Eikonalization of conformal blocks. United States. doi:10.1007/JHEP09(2015)019.
Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T., and Wang, Junpu. Thu . "Eikonalization of conformal blocks". United States. doi:10.1007/JHEP09(2015)019. https://www.osti.gov/servlets/purl/1225807.
@article{osti_1225807,
title = {Eikonalization of conformal blocks},
author = {Fitzpatrick, A. Liam and Kaplan, Jared and Walters, Matthew T. and Wang, Junpu},
abstractNote = {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.},
doi = {10.1007/JHEP09(2015)019},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2015,
place = {United States},
year = {2015},
month = {9}
}

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Cited by: 21 works
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    Works referencing / citing this record:

    Bootstrapping the (A1, A2) Argyres-Douglas theory
    journal, March 2018

    • Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro
    • Journal of High Energy Physics, Vol. 2018, Issue 3
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