Geometric constraints on the space of N $$ \mathcal{N} $$ = 2 SCFTs. Part 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 N $$ \mathcal{N} $$ = 2 SCFTs. In [1] we developed a strategy for classifying physical rank-1 CB geometries of N $$ \mathcal{N} $$ = 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 N f =4 su(2) gauge theory and the E n SCFTs which were constructed in [2, 3] and [4, 5].