Grant Elliot Final Defense

Abstract: Over the past few decades, the importance of non-Lagrangian quantum field theories has become increasingly recognized. These theories are very mysterious, but in the case of 4d theories with N=2 supersymmetry, they are somewhat tractable. We review general aspects of 4d N=2 SCFTs, with a focus on those originating from a 6d N=(2,0) theory, known as class-S theories. We then discuss how certain renormalization group flows, called nilpotent Higgsings, can help address various questions regarding these QFTs. In particular, we discuss their applications to determining invariants of 4d N=2 SCFTs, distinguishing between different 4d N=2 SCFTs, and the classification of such theories.