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

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.

28 pages

References in corpus (7)

• Mirrors of 3d Sicilian theories
• T^σ_ρ(G) Theories and Their Hilbert Series
• Branes and the Kraft-Procesi Transition
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours
• Algebraic properties of the monopole formula
• A characterization of nilpotent orbit closures among symplectic singularities II