On the moduli spaces of 4d $\mathcal{N}=3$ SCFTs I: triple special Kähler structure

Abstract

We initiate a systematic analysis of moduli spaces of vacua of four dimensional $\mathcal{N}=3$ SCFTs. Our analysis is based on the one hand on the properties of $\mathcal{N}=3$ chiral rings --- which we review in detail and contrast with chiral rings of theories with less supersymmetry --- and on the other hand on constraints coming from low-energy supersymmetry. This leads us to introduce a new type of geometric structure, which characterizes $\mathcal{N}=3$ SCFT moduli spaces, and that we call $triplespecialK\ddot{a}hler$ (TSK). A rank-$n$ TSK moduli space has complex dimension $3n$, and is singular at complex co-dimension 3 subspaces where charged states become massless. The structure of singularities defines a stratification of the TSK space in terms of lower-dimensional TSK manifolds.

arXiv comment70 pages

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Cited by in corpus (4)

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• A note on 4d N = 3 from little string theory
• The constraining power of Coulomb Branch Geometry: lectures on Seiberg-Witten theory
• The duality covariant geometry and DSZ quantization of abelian gauge theory