Speaker
Description
Partial wave decompositions are a central tool in the bootstrap approach to conformal field theory. In this talk, I will discuss differential equations that the partial waves satisfy. For a general $N$-point correlation function and a choice of an OPE channel, there is an associated Gaudin model with $N$ sites whose eigenfunctions coincide with the waves. This observation is a new instance of a relation between CFTs and quantum integrable systems, with potentially interesting implications for both. Two of the first applications will be described, which both originate from the OPE of the field theory: factorisation of higher-point partial waves into lower-point ones in an OPE limit, and reductions of the Gaudin model to elliptic and spinning hyperbolic Calogero-Moser-Sutherland models.
