Triangular Seminar Nadav Drukker (Humboldt)
A large family of interacting conformal field theories in four dimensions with N=2 supersymmetry was recently constructed by Gaiotto. Each gauge theory is associated to a Riemann surface with certain allowed singularities. In fact, it was proposed by Alday, Gaiotto and Tachikawa that the partition function of these theories (based on SU(2) gauge groups) is equal to correlation function in Liouville theory with central charge c=25. After reviewing these constructions I will turn to a detailed exploration of S-duality using loop operators: Wilson, 't Hooft and dyonic. I will explain the classification and evaluation of arbitrary loops in arbitrary theories and show how they transform into each-other under S-duality.