Deconfining $\mathcal{N}=2$ SCFTs, or the Art of Brane Bending

Abstract

We introduce a systematic approach to constructing $\mathcal{N}=1$ Lagrangians for a class of interacting $\mathcal{N}=2$ SCFTs. We analyse in detail the simplest case of the construction, arising from placing branes at an orientifolded $\mathbb{C}^2/\mathbb{Z}_2$ singularity. In this way we obtain Lagrangian descriptions for all the $R_{2,k}$ theories. The rank one theories in this class are the $E_6$ Minahan-Nemeschansky theory and the $C_2\times U(1)$ Argyres-Wittig theory. The Lagrangians that arise from our brane construction manifestly exhibit either the entire expected flavour symmetry group of the SCFT (for even $k$) or a full-rank subgroup thereof (for odd $k$), so we can compute the full superconformal index of the $\mathcal{N}=2$ SCFTs, and also systematically identify the Higgsings associated to partial closing of punctures.