Quiver Theories and Formulae for Slodowy Slices of Classical Algebras

Abstract

We utilise SUSY quiver gauge theories to compute properties of Slodowy slices; these are spaces transverse to the nilpotent orbits of a Lie algebra $\mathfrak{g}$. We analyse classes of quiver theories, with Classical gauge and flavour groups, whose Higgs branch Hilbert series are the intersections between Slodowy slices and the nilpotent cone $\mathcal{S}\cap \mathcal{N}$ of $\mathfrak{g}$. We calculate refined Hilbert series for Classical algebras up to rank $4$ (and $A_5$), and find descriptions of their representation matrix generators as algebraic varieties encoding the relations of the chiral ring. We also analyse a class of dual quiver theories, whose Coulomb branches are intersections $\mathcal{S}\cap \mathcal{N}$; such dual quiver theories exist for the Slodowy slices of $A$ algebras, but are limited to a subset of the Slodowy slices of $BCD$ algebras. The analysis opens new questions about the extent of $3d$ mirror symmetry within the class of SCFTs known as $T_{\sigma }^{\rho }(G)$ theories. We also give simple group theoretic formulae for the Hilbert series of Slodowy slices; these draw directly on the $SU(2)$ embedding into $G$ of the associated nilpotent orbit, and the Hilbert series of the nilpotent cone.

66 pages, 12 figures

References in corpus (11)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Counting Gauge Invariants: the Plethystic Program
• Mirrors of 3d Sicilian theories
• Quiver Subtractions
• T^σ_ρ(G) Theories and Their Hilbert Series
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Branes and the Kraft-Procesi Transition
• Highest Weight Generating Functions for Hilbert Series
• Branes and the Kraft-Procesi transition: classical case
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories

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• Variations on S-fold CFTs
• Quotient Quiver Subtraction
• Masses, Sheets and Rigid SCFTs
• Atomic Higgsings of 6D SCFTs
• $D_n$ Dynkin quiver moduli spaces
• Quiver Polymerisation
• Coulomb branch of a multiloop quiver gauge theory