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

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(l) for l = 1, 2, 3, 4, 6, and that the supersymmetry automatically enhances to N = 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 = 2 supersymmetric W-algebras.