Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories View Full Text


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Article Info

DATE

2018-08-29

AUTHORS

Amihay Hanany, Marcus Sperling

ABSTRACT

The Coulomb branches of certain 3-dimensional N=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} quiver gauge theories are closures of nilpotent orbits of classical or exceptional Lie algebras. The monopole formula, as Hilbert series of the associated Coulomb branch chiral ring, has been successful in describing the singular hyper-Kähler structure. By means of the monopole formula with background charges for flavour symmetries, which realises real mass deformations, we study the resolution properties of all (characteristic) height two nilpotent orbits. As a result, the monopole formula correctly reproduces (i) the existence of a symplectic resolution, (ii) the form of the symplectic resolution, and (iii) the Mukai flops in the case of multiple resolutions. Moreover, the (characteristic) height two nilpotent orbit closures are resolved by cotangent bundles of Hermitian symmetric spaces and the unitary Coulomb branch quiver realisations exhaust all the possibilities. More... »

PAGES

189

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    41 schema:description The Coulomb branches of certain 3-dimensional N=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N}=4 $$\end{document} quiver gauge theories are closures of nilpotent orbits of classical or exceptional Lie algebras. The monopole formula, as Hilbert series of the associated Coulomb branch chiral ring, has been successful in describing the singular hyper-Kähler structure. By means of the monopole formula with background charges for flavour symmetries, which realises real mass deformations, we study the resolution properties of all (characteristic) height two nilpotent orbits. As a result, the monopole formula correctly reproduces (i) the existence of a symplectic resolution, (ii) the form of the symplectic resolution, and (iii) the Mukai flops in the case of multiple resolutions. Moreover, the (characteristic) height two nilpotent orbit closures are resolved by cotangent bundles of Hermitian symmetric spaces and the unitary Coulomb branch quiver realisations exhaust all the possibilities.
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    47 schema:keywords Coulomb branch
    48 Coulomb branch chiral rings
    49 Hermitian symmetric spaces
    50 Hilbert series
    51 Kähler structure
    52 Lie algebra
    53 Mukai
    54 algebra
    55 background charge
    56 branches
    57 bundles
    58 cases
    59 charge
    60 chiral ring
    61 closure
    62 cotangent bundle
    63 deformation
    64 exceptional Lie algebras
    65 existence
    66 flavor symmetry
    67 form
    68 formula
    69 gauge theory
    70 mass deformation
    71 means
    72 monopole formula
    73 multiple resolutions
    74 nilpotent orbit closures
    75 nilpotent orbits
    76 orbit
    77 orbit closures
    78 possibility
    79 properties
    80 real mass deformation
    81 realisation
    82 resolution
    83 resolution properties
    84 results
    85 ring
    86 series
    87 space
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    93 schema:name Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4 theories
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