A. Liam Fitzpatrick, Jared Kaplan, David Poland, David Simmons-Duffin
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| << |v| < 1. We prove that every CFT with a scalar operator \phi\ must contain infinite sequences of operators O_{\tau,l} with twist approaching \tau -> 2\Delta_\phi\ + 2n for each integer n as l -> infinity. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the \phi\ x \phi\ 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 -> infinity. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.
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http://arxiv.org/abs/1212.3616
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