HET BROWN BAG SEMINAR | Expanding the Landscape of N=2 Super-Conformal Field Theories

In this talk I will argue that a systematic classification of 4d N=2 conformal field theories is possible through a careful analysis of the geometry of their Coulomb branches. I will carefully describe this general framework and then carry out the classification explicitly in the rank-1, that is one complex dimensional Coulomb branch, case. We find that the landscape of rank-1 theories is still largely unexplored and make a strong case for the existence of 8 (or up to 12) rank-1 SCFTs in addition to the 11 already known in the literature. De facto doubling the number of known rank-1 N=2 SCFTs. 4 of the 8 have been recently constructed using alternative methods and 3 of them have an intriguing enlarged, N=3, supersymmetry. Finally I will outline how to generalize our construction to higher rank, in particular to the rank-2 case.