Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits

TL;DR

This paper systematically studies the moduli spaces of nilpotent orbits for classical groups using quiver theories, providing new constructions, dualities, and detailed Hilbert series analyses up to rank 4.

Contribution

It offers a complete framework for BCD series nilpotent orbit moduli spaces, introduces new Coulomb branch constructions, and explores dualities and mirror symmetry in this context.

Findings

Systematic constructions for BCD series nilpotent orbits.

New Coulomb branch constructions for minimal nilpotent orbits.

Hilbert series and generating functions for orbit moduli spaces up to rank 4.

Abstract

We approach the topic of Classical group nilpotent orbits from the perspective of their moduli spaces, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of quiver theories defined by canonical partitions; this paper collects earlier work into a systematic framework, filling in gaps and providing a complete treatment. We find new Coulomb branch constructions for above minimal nilpotent orbits, including some based upon twisted affine Dynkin diagrams. We also discuss aspects of 3d mirror symmetry between these Higgs and Coulomb branch constructions and explore dualities and other relationships, such as HyperKahler quotients, between quivers. We analyse all Classical group nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert series and the Highest Weight Generating functions for their decompositions into characters of irreducible representations and/or Hall Littlewood polynomials.