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Title:
From Gaudin models to CFT: the integrability of multipoint conformal blocks
Speaker:
Abstract:
In this talk, I will review our recent progress on the characterization of multipoint conformal blocks in any spacetime dimension and any OPE channel. Our approach extends the standard four-point Casimir equations, introduced by Dolan and Osborn, to a set of higher-point eigenvalue equations of commuting operators that also measure quantum numbers associated with vertices of OPE diagrams. The relevant set of commuting operators can be recovered by special limits of Gaudin Hamiltonians, which reduce to a variety of integrable systems of Calogero-Moser-Sutherland type. Even in the absence of a complete solution, the system of differential equations that are constructed this way can be used to analyze systematically multipoint conformal blocks in special regimes, such as OPE and light-cone limits.
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