The Mellin formalism for boundary CFTd

We extend the Mellin representation of conformal field theory (CFT) to allow for conformal boundaries and interfaces. We consider the simplest holographic setup dual to an interface CFT - a brane filling an AdS(d) subspace of AdS(d+1) - and perform a systematic study of Witten diagrams in this setup. As a byproduct of our analysis, we show that geodesic Witten diagrams in this geometry reproduce interface CFTd conformal blocks, generalizing the analogous statement for CFTs with no defects.