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The analytic bootstrap and AdS superhorizon locality

Fitzpatrick, A. Liam and Kaplan, Jared and Poland, David and Simmons-Duffin, David (2013) The analytic bootstrap and AdS superhorizon locality. Journal of High Energy Physics, 2013 (12). Art. No. 004. ISSN 1029-8479. https://resolver.caltech.edu/CaltechAUTHORS:20170817-080656583

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Abstract

We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| ≪ |υ| < 1. We prove that every CFT with a scalar operator ϕ must contain infinite sequences of operators O_(τ,ℓ) with twist approaching τ → 2Δ_ϕ + 2n for each integer n as ℓ → ∞. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the ϕ × ϕ OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as ℓ → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/JHEP12(2013)004DOIArticle
https://arxiv.org/abs/1212.3616arXivDiscussion Paper
ORCID:
AuthorORCID
Poland, David0000-0003-3854-2430
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2013 SISSA, Trieste, Italy. Received: June 26, 2013. Accepted: November 22, 2013. Published: December 2, 2013. We are grateful to Sheer El-Showk, Ami Katz, Juan Maldacena, Miguel Paulos, João Penedones, Slava Rychkov, Alessandro Vichi, and Alexander Zhiboedov for discussions. We would also like to thank the participants of the “Back to the Bootstrap II” workshop for discussions and the Perimeter Institute for hospitality during the early stages of this work. ALF and JK thank the GGI in Florence for hospitality while this work was completed; JK also thanks the University of Porto. This material is based upon work supported in part by the National Science Foundation Grant No. 1066293. ALF was partially supported by ERC grant BSMOXFORD no. 228169. JK acknowledges support from the US DOE under contract no. DE-AC02-76SF00515.
Funders:
Funding AgencyGrant Number
NSFPHY-1066293
European Research Council (ERC)228169
Department of Energy (DOE)DE-AC02-76SF00515
Subject Keywords:Conformal and W Symmetry Nonperturbative Effects AdS-CFT Correspondence
Issue or Number:12
Record Number:CaltechAUTHORS:20170817-080656583
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170817-080656583
Official Citation:Fitzpatrick, A.L., Kaplan, J., Poland, D. et al. J. High Energ. Phys. (2013) 2013: 4. https://doi.org/10.1007/JHEP12(2013)004
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80548
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:17 Aug 2017 19:47
Last Modified:20 Nov 2020 20:06

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