High Energy Theory Seminar
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 many new rank-1 SCFTs, almost doubling the number of theories already known in the literature. The existence of 4 of them has been recently confirmed using alternative methods and others have an enlarged N=3, supersymmetry.
Most importantly the Coulomb branch analysis suggests the existence of a new N=4 SU(2) theory, with a different lattice of Wilson-'t Hooft line operators, which is self-dual under S-duality. I will spend the last part of my talk outlining the evidences supporting such an exciting possibility.