Multipoint Conformal Blocks in Conformal Field Theories

Abstract

A very powerful tool in Conformal Field Theories is the conformal block expansion, which plays a crucial role in the conformal bootstrap programme. The goal of this thesis is to improve the understanding and mathematical control over conformal block expansions for more than four external fields, studying the so-called multipoint conformal blocks from the perspective of the differential equations these satisfy. The results presented here stem from newly discovered relations between multipoint conformal blocks and Gaudin integrable models. These allow the introduction of special limits for multipoint conformal blocks which reduce them to some of their sub-components. Reduction to three-point blocks leads to a further novel connection between conformal blocks and integrable Calogero-Moser-Sutherland models. These results pave the way for future computations of multipoint conformal blocks, starting from certain well-behaved limits.