Deconfining $$ \mathcal{N} $$ = 2 SCFTs or the art of brane bending

Abstract

Abstract We introduce a systematic approach to constructing $$ \mathcal{N} $$ N = 1 Lagrangians for a class of interacting $$ \mathcal{N} $$ N = 2 SCFTs. We analyse in detail the simplest case of the construction, arising from placing branes at an orientifolded ℂ2/ℤ2 singularity. In this way we obtain Lagrangian descriptions for all the R2,k theories. The rank one theories in this class are the E6 Minahan-Nemeschansky theory and the C2 × 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 $$ \mathcal{N} $$ N = 2 SCFTs, and also systematically identify the Higgsings associated to partial closing of punctures.