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This is the second of a series of papers outlining an approach to theclassification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 viaa systematic analysis of their Coulomb branches, mathematically described byspecial K\"ahler scale invariant geometries. Here we describe how to make thetranslation between geometry and field theory data. We apply this strategy tothe special K\"ahler geometries found in the first paper of the series where wemade strong simplifying assumptions on the form of the solutions. Remarkably,we find that our bottom-up classification strategy pays off even in thissimplified setup. All scale invariant solutions in the first paper of theseries have an interpretation as the Coulomb branch of at least one$\mathcal{N}{=}2$ superconformal field theory, many matching what is alreadyknown. But we also predict the existence of six new rank 2 theories, includingan entire new set closed under renormalization group flow. We characterise anddiscuss in detail each one of these new $\mathcal{N}{=}2$ superconformal fieldtheories. To our knowledge none of them have known string theoretic or higherdimensional realisations.

The rank 2 classification problem II: mapping scale-invariant solutions to SCFTs