A “Lagrangian” for the E 7 superconformal theory

Abstract

Abstract We find an N=1 $$ \mathcal{N}=1 $$ gauge theory that flows to the rank-one N=2 $$ \mathcal{N}=2 $$ superconformal field theory with E 7 flavor symmetry. We first obtain a Lagrangian description for the R 0,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 0,4 theory. From this Lagrangian description, we compute the full superconformal index. We also consider twisted dimensional reduction on S 2 to obtain N=04 $$ \mathcal{N}=\left(0,4\right) $$ theory for the E 7 one instanton string and compute its elliptic genus.

Keywords

• Extended Supersymmetry
• Supersymmetric Gauge Theory
• Supersymmetry and Duality