### 4d SCFTs via discrete gauging

I will introduce the notion of discrete gauging in the context of 4d SCFTs and I will show how, using this procedure, we can obtain new SCFTs starting from 4d SCFTs mother theories. At the beginning of the talk I will review the mathematical tools that will be employed, that is to say the Superconformal index and the Higgs branch Hilbert series. I will then apply the discrete gauging in two different contexts. In the first case I will show how starting from $\mathcal{N}=4$ SYM, and discretely gauging a $\mathbb{Z}_n$ subgroup of the global symmetry group, we can obtain new $\mathcal{N}=4$ or $\mathcal{N}=3$ SCFTs (depending on the value of $n$). I will give a prescription for how to perform the discrete gauging at the level of the superconfomal index and Higgs branch Hilbert series. Finally I will give an overview of the results that we got in this context, in particular we will see that the Coulomb branches of the daughter theories generically are not-freely generated. Then I will focus on 4d SCFTs with $\mathcal{N}=2$ supersymmetry. In this context the mother theory will be always provided by a theory with SU(N), gauge group and the daughter theory will be obtained gauging the automorphism group of the Dynkin diagram. I will then analyse the consequences of this gauging. We will see that the global symmetry of the Higgs branch is modified in a non-trivial way and that, also for this class of theories, the corresponding Coulomb branch is generically not-freely generated.

The talk will be mainly based on the following two articles:

- "4d indices via discrete gauging", arXiv:1804.05396 .
- "The importance of Being Disconnected, A Principal Extension for Serious Groups", arXiv:1804.01108 .

**Tuesday, 12th of December 2018, 14:30, sala Wataghin**