Eikonalization of conformal blocks
Journal Article
·
· Journal of High Energy Physics (Online)
- 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.
- 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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