An N=1 Lagrangian for the rank 1 E6 superconformal theory

TL;DR

This paper proposes an $ ext{N}=1$ gauge theory that flows to a known strongly coupled $ ext{N}=2$ SCFT with $E_6$ symmetry, supported by anomaly and index comparisons, and extends the idea to a family of theories.

Contribution

It introduces a new $ ext{N}=1$ Lagrangian description for the rank 1 $E_6$ SCFT and generalizes to a broader class of models.

Findings

The proposed theory matches anomalies and superconformal index of the $E_6$ SCFT.

The framework extends to $ ext{SU}(2n+2)$ models with similar IR behavior.

Supports the existence of $ ext{N}=1$ Lagrangians for strongly coupled SCFTs.

Abstract

We propose that a certain $4d$ $\mathcal{N}=1$ $SU(4)$ gauge theory flows in the IR to the rank $1$ $\mathcal{N}=2$ strongly coupled SCFT with $E_6$ global symmetry and $25$ free chiral fields. This proposal is tested by comparing various RG invariant quantities, notably, anomalies and the superconformal index. We discuss the generalization to $\mathcal{N}=1$ $SU(2n+2)$ gauge theory models flowing in the IR to the $R_{(2,2n+1)}$ family of strongly coupled SCFTs plus free fields.