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This talk will elaborate on the manifestly crossing symmetric framework for studying the conformal bootstrap for a CFTd . This employs Witten diagrams of an auxiliary AdS d+1 . We will discuss how both exchange and contact Witten diagrams are necessary and also give simple, explicit representations/parametrisations of these in Mellin space. We will also show how explicit expressions for the crossing kernel for exchange Witten diagrams (i.e. the decomposition of a t-channel amplitude in s-channel partial waves) can be obtained in Mellin space. They are closely related to the generalised 6j-symbols and given in terms of 7F6 hypergeometric functions.
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