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 [1] 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 28 cases, with the exception of the Nf =4 su(2) gauge theory and the En SCFTs which were constructed in [2, 3] and [4, 5].
Highlights
Since the work of Seiberg and Witten [2, 3], a rich variety of techniques have been brought to bear in the study of the strong coupling dynamics of four dimensional supersymmetric N = 2 theories
In [1] we developed a strategy for classifying physical rank-1 Coulomb branch (CB) geometries of N = 2 SCFTs
In [1] we extensively describe our definition of physical consistency and carry out the complete classification of rank 1 CB geometries which includes all the known rank 1 N = 2 SCFTs plus sixteen new ones
Summary
This RG flow constraint requires that for particular values of the mass parameters determined by the detailed form of the SW curve, the singularity should split appropriately in a way dictated by the unbroken flavor group. Since evaluating this constraint requires the explicit construction of the CB geometry, it was only briefly discussed in [1], and is fully discussed here. We will, where convenient, switch between the standard and Dynkin names for the classical simple Lie algebras: An ⥠su(n + 1), Bn ⥠so(2n + 1), Cn ⥠sp(2n), Dn ⥠so(2n)
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