New Tools for New SCFTs

Recently, there has been a renewed interested in four-dimensional superconformal theories (SCFTs) which have no weakly coupled descriptions, even in the ultraviolet. Examples of such theories include those discovered by Gaiotto via wrapping M5-branes on a punctured Riemann surface, and also various SCFTs with exceptional global symmetries. I will give a toolbox for exploring such theories with N=1 supersymmetry, and discuss techniques for doing computations which do not rely on knowing any weak coupling description. As particular applications, I will discuss N=1 deformations of Gaiotto theories, as well as some exceptional SCFTs recently found via F-theory constructions.