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

Philip C. Argyres·Michael Crescimanno·Alfred D. Shapere·John R. Wittig
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Abstract

We study the classification of 2-dimensional scale-invariant rigid special Kahler (RSK) geometries, which potentially describe the Coulomb branches of N=2 supersymmetric field theories in four dimensions. We show that this classification is equivalent to the solution of a set of polynomial equations by using an integrability condition for the central charge, scale invariance, constraints coming from demanding single-valuedness of physical quantities on the Coulomb branch, and properties of massless BPS states at singularities. We find solutions corresponding to lagrangian scale invariant theories--including the scale invariant G_2 theory not found before in the literature--as well as many new isolated solutions (having no marginal deformations). All our scale-invariant RSK geometries are consistent with an interpretation as effective theories of N=2 superconformal field theories, and, where we can check, turn out to exist as quantum field theories.

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Philip C. Argyres, Michael Crescimanno, Alfred D. Shapere, John R. Wittig. 2005-06-01. Classification of N=2 Superconformal Field Theories with Two-Dimensional Coulomb Branches. https://arxiv.org/abs/hep-th/0504070

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