Operator spectroscopy for 4D SCFTs with a=c

Abstract

We study a rich set of four-dimensional superconformal field theories with both central charges identical: $a=c$. These are constructed via the diagonal $\mathcal{N}=2$ or $\mathcal{N}=1$ gauging of the flavor symmetry $G$ of a collection of $\mathcal{N}=2$ Argyres-Douglas theories of type ${\mathcal{D}}_{p}(G)$, with or without adjoint chiral multiplets, in 2106.12579 and 2111.12092. We compute superconformal indices of some theories where the rank of $G$ is low, performing a refined test for unitarity, and further determine the relevant and marginal operator content in detail. We find that most of these theories flow to interacting superconformal field theories with $a=c$ in the infrared.