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 [1] where singularities corresponding to curves of the form y2 = x6 with a fixed canonical basis of holomorphic one forms were analyzed. Here we perform the analysis for the y2 = x5 type singularities. (The final maximal singularity type, y2 = x3(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.