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Title: Holographic reconstruction of AdS exchanges from crossing symmetry

Abstract

Motivated by AdS/CFT, we address the following outstanding question in large N conformal field theory: given the appearance of a single-trace operator in the O x O OPE of a scalar primary O, what is its total contribution to the vacuum four-point function (OOOO) as dictated by crossing symmetry? We solve this problem in 4d conformal field theories at leading order in 1/N. Viewed holographically, this provides a field theory reconstruction of crossing-symmetric, four-point exchange amplitudes in AdS 5. Our solution takes the form of a resummation of the large spin solution to the crossing equations, supplemented by corrections at finite spin, required by crossing. The method can be applied to the exchange of operators of arbitrary twist τ and spin s, although it vastly simplifies for even-integer twist, where we give explicit results. The output is the set of OPE data for the exchange of all double-trace operators [OO] n,ℓ. We find that the double-trace anomalous dimensions γ n,ℓ are negative, monotonic and convex functions of ℓ, for all n and all ℓ > s. This constitutes a holographic signature of bulk causality and classical dynamics of even-spin fields. We also find that the “derivative relation” between double-trace anomalousmore » dimensions and OPE coefficients does not hold in general, and derive the explicit form of the deviation in several cases. Finally, we study large n limits of γ n,ℓ, relevant for the Regge and bulk-point regimes.« less

Authors:
 [1];  [2];  [3]
  1. Univ. of Oxford (United Kingdom). Mathematical Inst.
  2. Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature
  3. Princeton Univ., NJ (United States). Dept. of Physics
Publication Date:
Research Org.:
Princeton Univ., NJ (United States); Univ. of Oxford (United Kingdom); Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); European Research Council (ERC)
OSTI Identifier:
1425403
Grant/Contract Number:  
FG02-91ER40671; 306260
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: 2017; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 1/N expansion; conformal and W symmetry; conformal field theory

Citation Formats

Alday, Luis F., Bissi, Agnese, and Perlmutter, Eric. Holographic reconstruction of AdS exchanges from crossing symmetry. United States: N. p., 2017. Web. doi:10.1007/JHEP08(2017)147.
Alday, Luis F., Bissi, Agnese, & Perlmutter, Eric. Holographic reconstruction of AdS exchanges from crossing symmetry. United States. doi:10.1007/JHEP08(2017)147.
Alday, Luis F., Bissi, Agnese, and Perlmutter, Eric. Thu . "Holographic reconstruction of AdS exchanges from crossing symmetry". United States. doi:10.1007/JHEP08(2017)147. https://www.osti.gov/servlets/purl/1425403.
@article{osti_1425403,
title = {Holographic reconstruction of AdS exchanges from crossing symmetry},
author = {Alday, Luis F. and Bissi, Agnese and Perlmutter, Eric},
abstractNote = {Motivated by AdS/CFT, we address the following outstanding question in large N conformal field theory: given the appearance of a single-trace operator in the O x O OPE of a scalar primary O, what is its total contribution to the vacuum four-point function (OOOO) as dictated by crossing symmetry? We solve this problem in 4d conformal field theories at leading order in 1/N. Viewed holographically, this provides a field theory reconstruction of crossing-symmetric, four-point exchange amplitudes in AdS5. Our solution takes the form of a resummation of the large spin solution to the crossing equations, supplemented by corrections at finite spin, required by crossing. The method can be applied to the exchange of operators of arbitrary twist τ and spin s, although it vastly simplifies for even-integer twist, where we give explicit results. The output is the set of OPE data for the exchange of all double-trace operators [OO]n,ℓ. We find that the double-trace anomalous dimensions γ n,ℓ are negative, monotonic and convex functions of ℓ, for all n and all ℓ > s. This constitutes a holographic signature of bulk causality and classical dynamics of even-spin fields. We also find that the “derivative relation” between double-trace anomalous dimensions and OPE coefficients does not hold in general, and derive the explicit form of the deviation in several cases. Finally, we study large n limits of γ n,ℓ, relevant for the Regge and bulk-point regimes.},
doi = {10.1007/JHEP08(2017)147},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2017,
place = {United States},
year = {2017},
month = {8}
}

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    Works referencing / citing this record:

    The analytic functional bootstrap. Part II. Natural bases for the crossing equation
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