Analyticity in Spin in Conformal Theories

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The conformal bootstrap aims to calculate scaling dimensions and correlation functions in various theories, starting from general principles such as unitarity and crossing symmetry.  I will explain that local operators are not independent of each other but organize into analytic functions of spin, and I will present a formula which quantifies the consequences of this fact.  This will include a controlled approximation to the operator spectrum at large spin, as well as new bounds over the strength of bulk higher-derivative interactions in large-N theories with a sparse spectrum. These bounds, previously conjectured to exist using gauge-gravity duality, encode causality of the bulk theory.  Based on 1703.00278.