String Theory Seminar
Thursday, April 27, 2017, 3:00pm, 298 Physics (Physics Faculty Lounge)
Mikhail Isachenkov
Algebraic structures behind conformal blocks
Abstract:- 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.
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