The conformal block decomposition of conformal field theory (CFT) correlation functions has recently received renewed attention both due to its central role in the revival of the conformal bootstrap program, and also as a useful way to understand how local physics can emerge in the bulk in examples of AdS/CFT duality. In this talk I will discuss the relation between conformal blocks and anti-de Sitter gravity (AdS) through the AdS/CFT correspondence.
I will describe a new method for decomposing semi-classical gravity Feynman diagrams in AdS (Witten diagrams) intoconformal blocks. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is dubbed a "geodesic Witten diagram," and it provides an intuitive geometric bulk description of a conformal block. I will also present a unified framework for the holographic computation of Virasoroconformal blocks at large central charge.