An N=1 Lagrangian for an N=3 SCFT

TL;DR

This paper proposes a specific 4d N=1 gauge theory flows to an N=3 superconformal field theory with a rank 1 Coulomb branch, providing insights into its properties and potential generalizations.

Contribution

It introduces a new N=1 gauge theory that flows to an N=3 SCFT, and discusses properties and deformations of this SCFT, expanding understanding of such theories.

Findings

The IR limit of the proposed gauge theory is an N=3 SCFT with a rank 1 Coulomb branch.

The SCFT has a dimension three Coulomb branch operator.

The paper discusses RG invariants consistent with N=3 superconformal symmetry.

Abstract

We propose that a certain $4d$ $\mathcal{N}=1$ $SU(2)\times SU(2)$ gauge theory flows in the IR to an $\mathcal{N}=3$ SCFT plus a single free chiral field. The specific $\mathcal{N}=3$ SCFT has rank $1$ and a dimension three Coulomb branch operator. The flow is generically expected to land at the $\mathcal{N}=3$ SCFT deformed by the marginal deformation associated with said Coulomb branch operator. We also present a discussion about the properties expected of various RG invariant quantities from $\mathcal{N}=3$ superconformal symmetry, and use these to test our proposal. Finally, we discuss a generalization to another $\mathcal{N}=1$ model that we propose is related to a certain rank $3$ $\mathcal{N}=3$ SCFT through the turning of certain marginal deformations.