Speaker: Tomáš Procházka

Title: Integrability and Bethe equations in 2d CFT

Abstract: I want to discuss integrable aspects of two-dimensional conformal field theory (possibly extended by higher spin currents). It’s been known since 80s and 90s that Virasoro algebra admits infinite sets of local commuting conserved quantities (quantum KdV or BLZ charges). The associated Bethe equations look like equations for equilibrium positions of classical Calogero-like particles (ODE/IM correspondence). On the other hand, from more recent work on instantons in 4d supersymmetric gauge theories and AGT correspondence there are higher spin extensions of Virasoro algebra (W infinity or Yangian of affine gl(1)) whose Bethe equations are a simple generalization of su(2) XXX Heisenberg spin chain. It is rather surprising how these Bethe equations capture the rich representation theory of Virasoro algebra or its higher spin extensions.