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arXiv · 1707.09784

HWG for Coulomb branch of $3d$ Sicilian theory mirrors

Amihay Hanany·Alessandro Pini
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Abstract

Certain star shaped quivers exhibit a pattern of symmetry enhancement on the Coulomb branch of $3d$ $\mathcal{N}=4$ supersymmetric gauge theories. This paper studies a subclass of theories where such global symmetry enhancement occurs through a computation of the Highest Weight Generating Function (HWG) and of the corresponding Hilbert Series (HS), providing a further test of the Coulomb branch formula. This special subclass has a feature in which the HWG takes a particularly simple form, as a simple rational function which is either a product of simple poles (termed freely generated) or a simple PE (termed complete intersection). Out of all possible star shaped quivers, this is a particularly simple subclass. The present study motivates a further study of identifying all star shaped quivers for which their HWG is of this simple form.

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Amihay Hanany, Alessandro Pini. 2017-07-31. HWG for Coulomb branch of $3d$ Sicilian theory mirrors. https://arxiv.org/abs/1707.09784

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