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

Philip C. Argyres; Antoine Bourget; Mario Martone

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arXiv · 1912.04926

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

Philip C. Argyres·Antoine Bourget·Mario Martone

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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 $triple\ special\ Kähler$ (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.

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Philip C. Argyres, Antoine Bourget, Mario Martone. 2019-12-10. On the moduli spaces of 4d $\mathcal{N} = 3$ SCFTs I: triple special Kähler structure. https://arxiv.org/abs/1912.04926

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