A "Lagrangian" for the E7 Superconformal Theory

TL;DR

This paper constructs a Lagrangian for the E7 superconformal theory, enabling detailed analysis of its properties and related lower-dimensional theories, advancing understanding of exceptional symmetry in quantum field theories.

Contribution

It provides the first Lagrangian description for the E7 superconformal theory, derived from the R_{0,4} theory via partial Higgsing, and computes its superconformal index and elliptic genus.

Findings

Lagrangian description for E7 theory established

Superconformal index computed for the E7 theory

Elliptic genus calculated for the associated 2D 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 $R_{0, N}$ 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=(0, 4) theory for the $E_7$ one instanton string and compute its elliptic genus.