Deconfining Ν=2$ SCFTs or the Art of Brane Bending*

We introduce a systematic approach to constructing Ν=1 Lagrangians for a class of interacting Ν=2 SCFTs. A lot is known about the set of "class S" theories - four dimensional theories constructed by wrapping the six dimensional Ν=(2, 0) theories on Riemann surfaces with punctures - even if we don’t have explicit Lagrangians for most of them. By constructing a Lagrangian description for some of the theories in this class, we can check their properties, and often refine them. We analyse in detail the simplest case of the construction, arising from placing branes at an orientifolded C²/Z₂ singularity. This produces Lagrangian descriptions for all the R_2,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 Ν=2 SCFTs, and also systematically identify the Higgsings associated to partial closing of punctures.