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Simplifying large spin bootstrap in Mellin space

Dey, Parijat and Ghosh, Kausik and Sinha, Aninda (2018) Simplifying large spin bootstrap in Mellin space. In: JOURNAL OF HIGH ENERGY PHYSICS (1).

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Official URL: http://dx.doi.org/10.1007/JHEP01(2018)152

Abstract

We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations in terms of continuous Hahn polynomials, we derive explicit expressions as an asymptotic expansion in inverse conformal spin to any order, reproducing the contribution of any primary operator and its descendants in the crossed channel. The expressions are in terms of known mathematical functions and involve generalized Bernoulli (Norlund) polynomials and the Mack polynomials and enable us to derive certain universal properties. Comparing with the recently introduced reformulated equations in terms of crossing symmetric tree level exchange Witten diagrams, we show that to leading order in anomalous dimension but to all orders in inverse conformal spin, the equations are the same as in the conventional formulation. At the next order, the polynomial ambiguity in the Witten diagram basis is needed for the equivalence and we derive the necessary constraints for the same.

Item Type: Journal Article
Additional Information: Copy right for this article belong to the SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 02 Mar 2018 15:04
Last Modified: 02 Mar 2018 15:04
URI: http://eprints.iisc.ac.in/id/eprint/58947

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