Tomas Prochazka: Integrability in 2d CFT with higher spins

I will give an informal introduction to some aspects of quantum integrability in two-dimensional conformal field theory. The main focus will be on the Yangian-type structures that appear when the Virasoro symmetry is enlarged to higher-spin W-algebras. Starting from an R-matrix, one can use tools of quantum integrability to build families of commuting Hamiltonians and study their joint spectrum. I will explain how this leads to Bethe equations for CFT states, and how these equations may be viewed as a natural CFT analogue of the Bethe ansatz for the SU(2) XXX spin chain.