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The analytic bootstrap and AdS superhorizon locality

  • A. Liam Fitzpatrick
  • Jared KaplanEmail author
  • David Poland
  • David Simmons-Duffin
Article

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 \( {{\mathcal{O}}_{{\tau, \ell }}} \) with twist approaching τ → 2Δ ϕ + 2n for each integer n as → ∞. 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 → ∞. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.

Keywords

Conformal and W Symmetry Nonperturbative Effects AdS-CFT Correspondence 

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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • A. Liam Fitzpatrick
    • 1
  • Jared Kaplan
    • 1
    • 2
    Email author
  • David Poland
    • 3
  • David Simmons-Duffin
    • 4
  1. 1.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordUnited States
  2. 2.Department of Physics and AstronomyJohns Hopkins UniversityBaltimoreUnited States
  3. 3.Department of PhysicsYale UniversityNew HavenUnited States
  4. 4.School of Natural Sciences, Institute for Advanced StudyPrincetonUnited States

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