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 E7 flavor symmetry. We first obtain a Lagrangian description for the R0,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 E6 theory. The E7 theory is then obtained via partial Higgsing of the R0,4 theory. From this Lagrangian description, we compute the full superconformal index. We also consider twisted dimensional reduction on S2 to obtain N= (0 4) theory for the E7 one instanton string and compute its elliptic genus.