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Classification of N=2 Superconformal Field Theories with Two-Dimensional Coulomb Branches, II

Philip C. Argyres·John R. Wittig
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Abstract

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.

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Philip C. Argyres, John R. Wittig. 2005-10-26. Classification of N=2 Superconformal Field Theories with Two-Dimensional Coulomb Branches, II. https://arxiv.org/abs/hep-th/0510226

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