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.

70 pages

References in corpus (3)

• Branes and the Kraft-Procesi Transition
• Scaling dimensions of Coulomb branch operators of 4d N=2 superconformal field theories
• 4d N=2 SCFT and singularity theory Part III: Rigid singularity

Cited by in corpus (1)

• The constraining power of Coulomb Branch Geometry: lectures on Seiberg-Witten theory