Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows

Abstract

This is the second in a series of three papers on systematic analysis of rank 1 Coulomb branch geometries of four dimensional $\mathcal{N}$=2 SCFTs. In the first paper we developed a strategy for classifying physical rank-1 CB geometries of $\mathcal{N}$=2 SCFTs. Here we show how to carry out this strategy computationally to construct the Seiberg-Witten curves and one-forms for all the rank-1 SCFTs. Explicit expressions are given for all cases, with the exception of the $N_f$=4 SU(2) gauge theory and the En SCFTs which were previously constructed. Our classification includes all known rank-1 theories plus a new one with an abelian flavor group, plus nine additional theories whose existence is more speculative. Four of those, reported in our first paper, depend on the assumption of new frozen rank-1 SCFTs. Here we also also show that the assumption of the existence of certain rank-0 $\mathcal{N}$=2 SCFTs leads to five additional consistent rank-1 CB geometries.

Completely revised introduction and conclusion reflecting our current, deeper, understanding of the topic. Multiple references added

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• S-duality in N=2 supersymmetric gauge theories
• Tinkertoys for the Z3-twisted D4 Theory
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• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
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• Special Geometry and the Swampland
• Exceptional $\mathcal{N}=3$ theories
• Geometric constraints on the space of N=2 SCFTs III: enhanced Coulomb branches and central charges
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Compactifications of 5d SCFTs with a twist
• Mixed OPEs in $\mathcal{N}=2$ Superconformal Theories
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• Expanding the landscape of $\mathcal{N}$=2 rank 1 SCFTs
• The Partition Function Of Argyres-Douglas Theory On A Four-Manifold
• On the moduli spaces of 4d $\mathcal{N}=3$ SCFTs I: triple special Kähler structure
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• $\mathcal{N}=3$ four dimensional field theories