From Gaudin Integrable Models to $d$-dimensional Multipoint Conformal Blocks

Abstract

In this work we initiate an integrability-based approach to multipoint conformal blocks for higher dimensional conformal field theories. Our main observation is that conformal blocks for $N$-point functions may be considered as eigenfunctions of integrable Gaudin Hamiltonians. This provides us with a complete set of differential equations that can be used to evaluate multipoint blocks.

7 pages, 1 figure; added discussion of general dimensions and general number of points in comb channel