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Résumé |
I will explore a special subset of the 4d SCFT landscape, with N=1 and N=2 supersymmetry and identical central charges: a = c, without any large N limit. Such SCFTs are obtained via N=1 or N=2 diagonal gauging of collections of non-Lagrangian Argyres-Douglas and conformal matter theories and I will discuss the classification problem for consistent gaugings with interacting infrared SCFTs in both cases. For N=2 the classification is in terms of an ADE Dynkin diagram. Moreover, we find that the Schur indices for such theories can be written in terms of that of N=4 super-Yang-Mills theory upon rescaling fugacities. In particular, we find that the Schur index of the $\widehat{D}_4(SU(N))$ theory for N odd is written in terms of MacMahon's generalized sum-of-divisor function, which is quasimodular. Some such theories have a genus zero class S description, however their Higgs branch Hilbert series and Hall-Littlewood indices are different, providing a counterexample to a long-proposed conjecture. We find such examples are ubiquitous when there are at least four twisted punctures. We verify this distinction via multiple independent computations, including the study of the 3d mirrors of the class S theories. I will introduce each of these concepts and explain how they can be used to study the landscape of SCFTs and their features. |
