Conformal blocks from higher-point holography

Conformal blocks from higher-point holography

Abstract: Conformal blocks are theory-independent basic building blocks of local observables in conformal field theories (CFTs). They play an important role in the study of CFTs and in the context of holography.  Until recently, knowledge of higher-point (n>4) blocks was restricted to an extremely limited set of examples. In this talk I will present a simple set of "Feynman rules" for constructing all possible higher-point conformal blocks (involving external and exchanged scalars operators). These rules furnish explicit power-series expansions of blocks in powers of conformal cross-ratios. I will describe how to obtain this result via holography using position- and Mellin-space methods as well as crucial input from a discrete variant of holography.