On 4d rank-one N=3 superconformal field theories

TL;DR

$N=3$ SCFTs with rank one are shown to have moduli spaces of the form C^3/Zell with ell in {1,2,3,4,6}, with automatic enhancement to N=4 for ell in {1,2}. The central charges satisfy a=c=(2ell-1)/4, and the associated Beem-style 4d-to-2d correspondence yields exotic N=2 W-algebras as the 2d chiral algebras, with c2d = -3(2ell-1). The Higgs and Coulomb branches are tightly linked, and the 2d algebras are constrained by Jacobi identities, reproducing the Higgs branch relations W+ W- ~ J^ell via null states. These results illuminate the operator structure of potential genuine N=3 theories at ell=3,4,6 and establish a concrete 2d avatar for their protected sectors.

Abstract

We study the properties of 4d N=3 superconformal field theories whose rank is one, i.e. those that reduce to a single vector multiplet on their moduli space of vacua. We find that the moduli space can only be of the form C^3/Z_k for k=1,2,3,4,6, and that the supersymmetry automatically enhances to N=4 for k=1,2. In addition, we determine the central charges a and c in terms of k, and construct the associated 2d chiral algebras, which turn out to be exotic N=2 supersymmetric W-algebras.