Classification of N=2 Superconformal Field Theories with Two-Dimensional   Coulomb Branches, II
  We continue the classification of 2-dimensional scale-invariant rigid special Kahler (RSK) geometries. This classification was begun in [hep-th/0504070] where singularities corresponding to curves of the form y^2=x^6 with a fixed canonical basis of holomorphic one forms were analyzed. Here we perform the analysis for the y^2=x^5 type singularities. (The final maximal singularity type, y^2=x^3(x-1)^3, will be analyzed in a later paper.) These singularities potentially describe the Coulomb branches of N=2 supersymmetric field theories in four dimensions. We show that there are only 13 solutions satisfying the integrability condition (enforcing the RSK geometry of the Coulomb branch) and the Z-consistency condition (requiring massless charged states at singularities). Of these solutions, one has a marginal deformation, and corresponds to the known solution for certain Sp(2) gauge theories, while the rest correspond to isolated strongly interacting conformal field theories. 
Philip C. Argyres and John R. Wittig