Abstract
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.
Highlights
Introduction.—Conformal field theories (CFTs) are central to our modern understanding of strongly interacting systems in high energy physics, condensed matter physics, and statistical mechanics
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 framework allows us to connect with the conceptually rich picture of the Polyakov blocks being identified with Witten diagrams in anti-de Sitter space
Summary
Introduction.—Conformal field theories (CFTs) are central to our modern understanding of strongly interacting systems in high energy physics, condensed matter physics, and statistical mechanics. Crossing Symmetric Dispersion Relations for Mellin Amplitudes We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories.
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