A "Lagrangian" for the E-7 superconformal theory

Abstract

We find an N = 1 gauge theory that flows to the rank-one N = 2 superconformal field theory with E-7 flavor symmetry. We first obtain a Lagrangian description for the R-0,R-N theory, which appears in the S-dual description of the SU(N) gauge theory with 2N fundamental hypermultiplets. This is a straightforward generalization of the proposed Lagrangian description for the E-6 theory. The E-7 theory is then obtained via partial Higgsing of the R-0,R-4 theory. From this Lagrangian description, we compute the full superconformal index. We also consider twisted dimensional reduction on S-2 to obtain N = (0, 4) theory for the E7 one instanton string and compute its elliptic genus.