On the Polyakov-Mellin bootstrap

Rajesh Gopakumar, Aninda Sinha
2018 Journal of High Energy Physics  
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
more » ... alternate simplified representations of the Witten diagrams in Mellin space. This enables us to also obtain compact, explicit expressions (in terms of a _7F_6 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.
doi:10.1007/jhep12(2018)040 fatcat:kpahzfl5fzfg3o6umohakuetwa