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Crossing Symmetric Dispersion Relations for Mellin Amplitudes

Gopakumar, R and Sinha, A and Zahed, A (2021) Crossing Symmetric Dispersion Relations for Mellin Amplitudes. In: Physical Review Letters, 126 (21).

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Official URL: https://doi.org/10.1103/PhysRevLett.126.211602


We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories. This allows us to set up the nonperturbative Polyakov bootstrap for the conformal field theories in Mellin space on a firm foundation, thereby fixing the contact term ambiguities in the crossing symmetric blocks. Our new approach employs certain "locality"constraints replacing the requirement of crossing symmetry in the usual fixed-t dispersion relation. Using these constraints, we show that the sum rules based on the two channel dispersion relations and the present dispersion relations are identical. Our framework allows us to connect with the conceptually rich picture of the Polyakov blocks being identified with Witten diagrams in anti-de Sitter space. We also give two sided bounds for Wilson coefficients for effective field theories in anti-de Sitter space. © 2021 authors.

Item Type: Journal Article
Publication: Physical Review Letters
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to Authors
Keywords: Correlators; Quantum theory, Conformal field theories; Dispersion relations; Effective field theory; Four-point; New approaches; Nonperturbative; Rich picture; Two channel, Dispersions
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 19 Aug 2021 10:12
Last Modified: 19 Aug 2021 10:12
URI: http://eprints.iisc.ac.in/id/eprint/69248

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