Magnetic Lattices for Orthosymplectic Quivers

Abstract

For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the identification of the precise gauge group becomes crucial when the magnetic spectrum of the theory is considered. This question is addressed in the context of Coulomb branches for $3$d $\mathcal{N}=4$ quiver gauge theories, which are moduli spaces of dressed monopole operators. Since monopole operators are characterized by their magnetic charge, the identification of the gauge group is imperative for the determination of the magnetic lattice. It is well-known that the gauge group of unframed unitary quivers is the product of all unitary nodes in the quiver modded out by the diagonal $\mathrm{U}(1)$ acting trivially on the matter representation. This reasoning generalises to the notion that a choice of gauge group associated to a quiver is given by the product of the individual nodes quotiented by any subgroup that acts trivially on the matter content. For unframed (unitary-) orthosymplectic quivers composed of $\mathrm{SO}(\text{even})$, $\mathrm{USp}$, and possibly $\mathrm{U}$ gauge nodes, the maximal subgroup acting trivially is a diagonal ${\mathbb{Z}}_2$. For unframed unitary quivers with a single $\mathrm{SU}(N)$ node it is ${\mathbb{Z}}_N$. We use this notion to compute the Coulomb branch Hilbert series of many unitary-orthosymplectic quivers. Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics. This includes Higgs branches of theories with 8 supercharges in dimensions $4$, $5$, and $6$. A crucial ingredient in the calculation of exact refined Hilbert series is the alternative construction of unframed magnetic quivers from resolved Slodowy slices, whose Hilbert series can be derived from Hall-Littlewood polynomials.

arXiv commentv2: 44 pages + appendices, matches JHEP version, added references and fixed typos

References in corpus (56)

• Generalized Global Symmetries
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Reading between the lines of four-dimensional gauge theories
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• Counting Gauge Invariants: the Plethystic Program
• 6d Conformal Matter
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Branes and Six Dimensional Supersymmetric Theories
• Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
• Mirrors of 3d Sicilian theories
• Branes at Orbifolds versus Hanany Witten in Six Dimensions
• Monopole Operators and Mirror Symmetry in Three Dimensions
• Tinkertoys for Gaiotto Duality
• New Phases of String Theory and 6d RG Fixed Points via Branes at Orbifold Singularities
• 3d dualities from 4d dualities for orthogonal groups
• The Hilbert Series of the One Instanton Moduli Space
• Tinkertoys for the D_N series
• RG Fixed Points in Six Dimensions via Branes at Orbifold Singularities
• Branes and Six Dimensional Fixed Points
• The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities
• Brane webs and $O5$-planes
• Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
• 3d Coulomb branch and 5d Higgs branch at infinite coupling
• Quiver Subtractions
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
• Instanton Operators and the Higgs Branch at Infinite Coupling
• Membranes and Fivebranes with Lower Supersymmetry and their AdS Supergravity Duals
• Line Operators in the Standard Model
• Monopole operators in three-dimensional N=4 SYM and mirror symmetry
• 6d SCFTs, 5d Dualities and Tao Web Diagrams
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
• Magnetic quivers for rank 1 theories
• Highest Weight Generating Functions for Hilbert Series
• Hilbert Series for Moduli Spaces of Two Instantons
• Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits
• Discrete Gauging in Six Dimensions
• Magnetic Quivers, Higgs Branches, and 6d N=(1,0) Theories -- Orthogonal and Symplectic Gauge Groups
• Mirror symmetry by O3-planes
• Magnetic Quivers from Brane Webs with O5 Planes
• N=1 dynamics with T_N theory
• The Small $E_8$ Instanton and the Kraft Procesi Transition
• Branes and the Kraft-Procesi transition: classical case
• Higgs branch, HyperKahler quotient and duality in SUSY N=2 Yang-Mills theories
• Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras
• Hasse Diagrams for $3d$ $\mathcal{N}=4$ Quiver Gauge Theories -- Inversion and the full Moduli Space
• Discrete Gauging in Coulomb branches of Three Dimensional $\mathcal{N}=4$ Supersymmetric Gauge Theories
• Discrete quotients of 3-dimensional N = 4 Coulomb branches via the cycle index
• Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories
• Quiver Theories and Hilbert Series of Classical Slodowy Intersections
• Quiver Theories and Formulae for Slodowy Slices of Classical Algebras
• Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver Theories
• Nilpotent orbits and the Coulomb branch of $T^{\sigma }(G)$ theories: special orthogonal vs orthogonal gauge group factors
• Comments on the twisted punctures of $A_{\text{even}}$ class S theory
• Minimally Unbalanced Quivers
• Towards Deconstruction of the Type D (2,0) Theory

Cited by in corpus (28)

• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions
• S-fold magnetic quivers
• Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations
• Magnetic quivers for rank 2 theories
• Folding Orthosymplectic Quivers
• Balanced B and D-type orthosymplectic quivers -- Magnetic quivers for product theories
• Conformal Manifolds and 3d Mirrors of Argyres-Douglas theories
• Higgs Branches of U/SU Quivers via Brane Locking
• Factorised 3d $\mathcal{N}=4$ orthosymplectic quivers
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Magnetic quivers and negatively charged branes
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Higgs branch RG-flows via Decay and Fission
• Decay and Fission of Magnetic Quivers
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Discrete gauging and Hasse diagrams
• Exploring the orthosymplectic zoo
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Orthosymplectic Implosions
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• On non-supersymmetric fixed points in five dimensions
• Orthosymplectic Quotient Quiver Subtraction
• Atomic Higgsings of 6D SCFTs
• Complex Symplectic Contractions and 3d Mirrors
• Quiver Polymerisation
• FI-flows of 3d N=4 Theories