Analyticity in spin in conformal theories

By S. Caron-Huot. Journal of High Energy Physics, 2017

459 citations recorded by the source corpus.

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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/08272ccb83468277e984049a4637588580fd318b

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Citations in the corpus

• Weight shifting operators and conformal blocks (2017, unknown): “For example, one can derive spinning versions of the CFT Froissart-Gribov formula [90] using these techniques.”
• Bootstrapping inflationary correlators in Mellin space (2019, background): “These comprise a complete basis of single-valued orthogonal Eigenfunctions of the Casimir invariants for the Conformal group [16, 17, 113, 114].”