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A Mellin space approach to the conformal bootstrap

Gopakumar, Rajesh and Kaviraj, Apratim and Sen, Kallol and Sinha, Aninda (2017) A Mellin space approach to the conformal bootstrap. In: JOURNAL OF HIGH ENERGY PHYSICS (5).

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Official URL: http://dx.doi.org/ 10.1007/JHEP05(2017)027

Abstract

We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of CFTd four point functions and expands them in terms of crossing symmetric combinations of AdS(d+1) Witten exchange functions. We consider arbitrary external scalar operators and set up the conditions for consistency with the operator product expansion. Namely, we demand cancellation of spurious powers (of the cross ratios, in position space) which translate into spurious poles in Mellin space. We discuss two contexts in which we can immediately apply this method by imposing the simplest set of constraint equations. The first is the epsilon expansion. We mostly focus on the Wilson-Fisher fixed point as studied in an epsilon expansion about d = 4. We reproduce Feynman diagram results for operator dimensions to O(epsilon(3)) rather straightforwardly. This approach also yields new analytic predictions for OPE coefficients to the same order which fit nicely with recent numerical estimates for the Ising model (at epsilon = 1). We will also mention some leading order results for scalar theories near three and six dimensions. The second context is a large spin expansion, in any dimension, where we are able to reproduce and go a bit beyond some of the results recently obtained using the (double) light cone expansion. We also have a preliminary discussion about numerical implementation of the above bootstrap scheme in the absence of a small parameter.

Item Type: Journal Article
Additional Information: Copy right for this article belongs 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: review EPrints Reviewer
Date Deposited: 13 Jan 2018 05:55
Last Modified: 13 Jan 2018 05:55
URI: http://eprints.iisc.ac.in/id/eprint/58613

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