On 4d rank-one N = 3 $$ mathcal{N}=3 $$ superconformal field theories

Abstract

We study the properties of 4d N=3N=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 ℂ3/ℤℓ for ℓ=1, 2, 3, 4, 6, and that the supersymmetry automatically enhances to N=4N=4 for ℓ=1, 2. In addition, we determine the central charges a and c in terms of ℓ, and construct the associated 2d chiral algebras, which turn out to be exotic N=2N=2 supersymmetric W-algebras.