Holographic reconstruction of AdS exchanges from crossing symmetry
Motivated by AdS/CFT, we address the following outstanding question in large N conformal field theory: given the appearance of a singletrace operator in the O x O OPE of a scalar primary O, what is its total contribution to the vacuum fourpoint 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 crossingsymmetric, fourpoint 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 eveninteger twist, where we give explicit results. The output is the set of OPE data for the exchange of all doubletrace operators [OO] _{n,ℓ}. We find that the doubletrace 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 evenspin fields. We also find that the “derivative relation” between doubletrace anomalousmore »
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Univ. of Oxford (United Kingdom). Mathematical Inst.
 Harvard Univ., Cambridge, MA (United States). Center for the Fundamental Laws of Nature
 Princeton Univ., NJ (United States). Dept. of Physics
 Publication Date:
 Grant/Contract Number:
 FG0291ER40671; 306260
 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 10298479
 Publisher:
 Springer Berlin
 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) (SC25); European Research Council (ERC)
 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
 OSTI Identifier:
 1425403
Alday, Luis F., Bissi, Agnese, and Perlmutter, Eric. Holographic reconstruction of AdS exchanges from crossing symmetry. United States: N. p.,
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. 2017.
"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 singletrace operator in the O x O OPE of a scalar primary O, what is its total contribution to the vacuum fourpoint 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 crossingsymmetric, fourpoint 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 eveninteger twist, where we give explicit results. The output is the set of OPE data for the exchange of all doubletrace operators [OO]n,ℓ. We find that the doubletrace 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 evenspin fields. We also find that the “derivative relation” between doubletrace 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 bulkpoint 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}
}