In this seminar I will discuss a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. We show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in detail the mechanism underlying this phenomenon and formulate a simple criterion for supersymmetry enhancement.

In this seminar I will discuss a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. We show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in detail the mechanism underlying this phenomenon and formulate a simple criterion for supersymmetry enhancement.

In this talk I will discuss superconformal theories in four dimensions obtained wrapping M5 branes on a Riemann surface. I will first review N=2 class S theories introduced some years ago by Gaiotto and then describe a generalization to the N=1 case. For this class of theories it is possible to write down a spectral curve encoding the properties of the chiral ring and I propose a method to determine from the spectral curve the scaling dimension of chiral operators in the SCFT. This proposal reduces to the correct prescription in the special case of N=2 theories. I will provide several consistency checks and apply this method to study some new superconformal theories.