title: Superintegrability of d-Dimensional Conformal Blocks.
abstract: We observe that conformal blocks of scalar four-point functions in a d-dimensional conformal field theory can be mapped to eigenfunctions of a two-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled Pöschl-Teller particles. Their interaction, whose strength depends smoothly on the dimension d, is known to be superintegrable. Our observation enables us to exploit the rich mathematical literature on Calogero-Sutherland models in deriving various results for conformal field theory. These include an explicit construction of conformal blocks in terms of Heckman-Opdam hypergeometric functions. We conclude with a short outlook, in particular, on the consequences of integrability for the theory of conformal blocks.
authors: Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 7610001, Israel.
authors: Mikhail
authors: M
authors: Isachenkov
authors: DESY Theory Group, DESY Hamburg, Notkestrasse 85, D-22603 Hamburg, Germany.
authors: Volker
authors: V
authors: Schomerus