Highest weight generating functions for Hilbert series

Zafrir

2018

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139

When n M5 branes coincide on an A type singularity, C 2 /Z k , there is a multitude of tensionless strings which arise in the spectrum. The low energy theory when all M5 branes are separated at the singularity is given by a linear quiver with parameters n and k. The theory has a multitude of phases, as many as partitions of n, each characterized by a different Higgs branch. Each such Higgs branch can be described by a Coulomb branch of a 3d N = 4 quiver. For example, at finite coupling, when all branes are separated, the quiver has a bouquet of n U(1) nodes connected to a single node. There is a natural discrete non Abelian S n global symmetry which acts in the theory by permuting n identical objects. It acts in particular on the Higgs branch at the above finite coupling phase. It is conjectured that at the coincident point this discrete S n flavor symmetry is gauged, and at partial coincidence the corresponding subgroup of S n is gauged. This elegant and simple effect solves several problems which are raised recently on the physics of multiple M5 branes on an A type singularity. Similar results on multitude of phases are concluded for a system of n M5 branes on an A type singularity next to an M9 plane.

Section: Jhep07(2018)168mentioning

confidence: 99%

Discrete gauging in six dimensions

Zafrir

2018

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139

“…This compact form is given by the Highest Weight Generating function (HWG), [14]. The HWGs for the first two families of quivers have simple forms and are therefore included.…”

Section: Jhep08(2018)158mentioning

confidence: 99%

Discrete gauging in Coulomb branches of three dimensional $$ \mathcal{N}=4 $$ supersymmetric gauge theories

Zajac

2018

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This paper tests a conjecture on discrete non-Abelian gauging of 3d N = 4 supersymmetric quiver gauge theories. Given a parent quiver with a bouquet of n nodes of rank 1, invariant under a discrete S n global symmetry, one can construct a daughter quiver where the bouquet is substituted by a single adjoint n node. Based on the main conjecture in this paper, the daughter quiver corresponds to a theory where the S n discrete global symmetry is gauged and the new Coulomb branch is a non-Abelian orbifold of the parent Coulomb branch. We demonstrate and test the conjecture for three simply laced families of bouquet quivers and a non-simply laced bouquet quiver with C 2 factor in the global symmetry.

“…We choose to approach the topic of nilpotent orbits from the perspective of their moduli spaces and Hilbert series, which we analyse using the tools of the Plethystics Program [8,9]. Each such Hilbert series counts holomorphic functions on the closure of a nilpotent orbit [10].…”

Section: Jhep06(2016)130mentioning

confidence: 99%

Quiver theories for moduli spaces of classical group nilpotent orbits

Kalveks

2016

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174

Abstract:We approach the topic of Classical group nilpotent orbits from the perspective of the moduli spaces of quivers, 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 HyperKähler 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.