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

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.

20 pages

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• 3d N=4 Bootstrap and Mirror Symmetry
• Conformal S-dualities from O-planes
• Emergent N=4 supersymmetry from N=1
• Rank $Q$ E-String on Spheres with Flux
• Vanishing short multiplets in rank one 4d/5d SCFTs
• Aspects of 4d supersymmetric dynamics and geometry