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Journal of High Energy Physics

, 2018:40 | Cite as

On the Polyakov-Mellin bootstrap

  • Rajesh Gopakumar
  • Aninda SinhaEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We elaborate on some general aspects of the crossing symmetric approach of Polyakov to the conformal bootstrap, as recently formulated in Mellin space. This approach uses, as building blocks, Witten diagrams in AdS. We show the necessity for having contact Witten diagrams, in addition to the exchange ones, in two different contexts: a) the large c expansion of the holographic bootstrap b) in the ϵ expansion at subleading orders to the ones studied already. In doing so, we use alternate simplified representations of the Witten diagrams in Mellin space. This enables us to also obtain compact, explicit expressions (in terms of a 7F6 hypergeometric function!) for the analogue of the crossing kernel for Witten diagrams i.e., the decomposition into s-channel partial waves of crossed channel exchange diagrams.

Keywords

AdS-CFT Correspondence Conformal Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.International Centre for Theoretical Sciences (ICTS-TIFR)Bangalore NorthIndia
  2. 2.Centre for High Energy Physics, Indian Institute of ScienceBangaloreIndia

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