Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4$$ mathcal{N}=4 $$ theories
Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional N=4$$ mathcal{N}=4 $$ theories
复制标题
通过 3 维 N=4$$ mathcal{N}=4 $$ 理论的库仑分支求解幂零轨道闭包
DOI：
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发表时间：
2018
影响因子：
5.4
通讯作者：
Marcus Sperling
中科院分区：
文献类型：
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作者：
A. Hanany;Marcus Sperling
某些三维N=4$ mathcal{N}=4 $$mathcal规范理论的库仑支是经典或例外李代数的幂零轨道的闭包。作为库仑分支手征环的Hilbert级数，Escherberg公式成功地描述了奇异超Kähler结构.利用味对称性的带背景电荷的单极公式，实现了真实的质量变形，研究了所有（特征）高度为2的幂零轨道的分辨性质。因此，该公式正确地再现了（i）辛解析的存在性，（ii）辛解析的形式，以及（iii）多重解析情况下的Mukai触发器。此外，（特征）高度2幂零轨道闭包解决了余切丛厄米对称空间和酉库仑分支实现穷尽了所有的可能性。
A bstractThe Coulomb branches of certain 3-dimensional N=4$$ mathcal{N}=4 $$ 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.