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The analytic bootstrap and AdS superhorizon locality

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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 \( {{\mathcal{O}}_{{\tau, \ell }}} \) 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.

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Authors and Affiliations

  1. Stanford Institute for Theoretical Physics, Stanford University, Stanford, CA, 94305, United States

    A. Liam Fitzpatrick & Jared Kaplan

  2. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, 21218, United States

    Jared Kaplan

  3. Department of Physics, Yale University, New Haven, CT, 06520, United States

    David Poland

  4. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, United States

    David Simmons-Duffin

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  1. A. Liam Fitzpatrick
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  2. Jared Kaplan
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  4. David Simmons-Duffin
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Correspondence to Jared Kaplan.

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ArXiv ePrint: 1212.3616

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Fitzpatrick, A.L., Kaplan, J., Poland, D. et al. The analytic bootstrap and AdS superhorizon locality. J. High Energ. Phys. 2013, 4 (2013). https://doi.org/10.1007/JHEP12(2013)004

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