Algebraic structures behind conformal blocks

String Theory Seminar

Mikhail Isachenkov

Thursday, April 27, 2017 -
3:00pm to 4:00pm
Location: 
298 Physics (Physics Faculty Lounge)

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 suggests that a uniform treatment of conformal blocks with spin is possible via this approach.