A plethora of K3 metrics
arXiv:2010.12581
Abstract
We extend our recent study of K3 metrics near the orbifold locus to the other torus orbifold loci. In particular, we provide several new constructions of K3 surfaces as hyper-Kähler quotients, which yield new formulae for K3 metrics. We then relate these to the construction of arXiv:1810.10540. As a corollary, we derive infinitely many constraints on the (as yet unknown) BPS spectra of the Minahan-Nemeschansky SCFTs with global symmetry. Specifically, we find linear combinations of characters (evaluated at different points) hiding within K3 metrics and we compute their second order Taylor expansions. We also find novel strong relationships between the BPS spectra of these SCFTs, as well as with that of the SCFT. Finally, we provide a new derivation of the class S constructions of these SCFTs and state some experimental observations regarding their BPS spectra.
arXiv comment72 pages
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