Conformal Blocks and Integrability

by Prof. Mikhail Isachenkov (Weizmann Institute of Science & IHES)

Thursday Dec 21, 2017, 2:30 PM → 3:30 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

I will discuss a relation between conformal blocks, describing kinematics of a CFT, and integrable models of quantum-mechanical particles. I will show how the dependence of blocks on cross-ratios is encoded in equations of motion of a Calogero-Sutherland model and their dependence on conformal dimension and spin of the exchanged operator - in those of a relativistic Calogero-Sutherland model. Both are simultaneously controlled by an integrable connection generalizing 2d Knizhnik-Zamolodchikov equations. I will review how this connection, associated to representations of degenerate double affine Hecke algebra, comes from a q-deformed bispectrally symmetric setting.