On the Polyakov-Mellin bootstrap

Understand

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 $\epsilon$ expansion at subleading orders to the ones studied already.
• In doing so, we use alternate simplified representations of the Witten diagrams in Mellin space.