String Theory Journal Club
sala 5.42, ul. Pasteura 5
2017-04-24 (11:00) 
Marcin Piątek (University of Szczecin)
2d CFT, N=2 gauge theories and solvable spectral problems
The so-called 2d/4d correspondences connect two-dimensional conformal field theory (2d CFT), N=2 supersymmetric gauge theories and quantum integrable systems. The latter in the simplest case of SU(2) gauge group are just quantum–mechanical systems. During seminar it will be shown how these dualities can be used, in particular, to study the spectra of Schroedinger operators with periodic (Hill's), PT-symmetric and elliptic (finite-gap) potentials. Moreover, it will be mentioned that an application of 2d CFT technics and tools such as (classical) conformal bootstrap paves the way for studying nonperturbative effects in afforementioned quantum-mechanical systems. Finally, some open problems such as the relation to the KdV theory will be mentioned as well