March 28, 2017 @ 12:00 pm – 12:35 pm
Integrability of Conformal Blocks
We 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 simultaneosly controlled by an integrable connection generalizing 2d Knizhnik-Zamolodchikov equations. The connection is associated to representations of degenerate double affine Hecke algebra, which allows for a uniform treatment of conformal blocks with spin via this approach.