Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP09(2017)078
Keywords
Conformal Field Theory; Conformal and W Symmetry; AdS-CFT Correspondence
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Conformal theory correlators are characterized by the spectrum and three-point functions of local operators. We present a formula which extracts this data as an analytic function of spin. In analogy with a classic formula due to Froissart and Gribov, it is sensitive only to an imaginary part which appears after analytic continuation to Lorentzian signature, and it converges thanks to recent bounds on the high-energy Regge limit. At large spin, substituting in cross-channel data, the formula yields 1/J expansions with controlled errors. In large-N theories, the imaginary part is saturated by single-trace operators. For a sparse spectrum, it manifests the suppression of bulk higher-derivative interactions that constitutes the signature of a local gravity dual in Anti-de-Sitter space.
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