Ungauging schemes and Coulomb branches of non-simply laced quiver theories
Ungauging schemes and Coulomb branches of non-simply laced quiver theories
复制标题
非简单带状箭袋理论的测量方案和库仑分支
DOI：
10.1007/jhep09(2020)193
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发表时间：
2020
影响因子：
5.4
通讯作者：
A. Zajac
中科院分区：
文献类型：
--
作者：
A. Hanany;A. Zajac
三维库仑支在 3、4、5 和 6 维 8 个超荷的超对称规范理论的模空间研究中发挥着重要作用。灵感来自于简单的 3d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 4 个超对称箭袋规范理论，我们考虑由具有边缘重数 k 且无风味节点的非简单系带箭袋构造的库仑分支。在将库仑支计算为修饰单极子算子的空间时，需要取消质心 U(1) 对称性。通常，对于简单的理论，未计量 U(1) 的所有选择（即未计量方案的所有选择）都是等效的，并且库仑分支是唯一的。在本文中，我们研究了各种非测量方案及其对所得库仑分支变化的影响。结果表明，对于非简单系带箭袋，存在对应于不等库仑分支变体的不等价测量方案。对非简单系带箭袋的任何长节点进行测量都会产生相同的库仑分支 C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{文档}$$ \mathcal{C} $$\end{文档}。对于在秩高于 1 的短节点上取消测量 U(1) 的选择，GNO 双磁晶格会发生各向异性变形，使其不再对应于李群，因此单极子公式会产生无效的库仑分支。然而，如果在秩 1 的短节点上执行测量，则一维磁晶格沿其单一方向（即各向同性）重新缩放，并且相应的库仑分支是形式为 C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} 的轨道折叠\usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{C} $$\end{document}/ℤk 。 3d 库仑分支的测量方案为 Kostant 和 Brylinski [1] 研究的幂零轨道上的作用子集提供了特别有趣且直观的描述。对最小不平衡 Cn、仿射 F4、仿射 G2 和扭曲仿射 D43\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} 进行非测量方案分析\setlength{\oddsidemargin}{-69pt} \begin{document}$$ {D}_4^{(3)} $$\end{document} 分别颤抖。该分析通过最高权重生成函数的计算得到补充。
Three dimensional Coulomb branches have a prominent role in the study of moduli spaces of supersymmetric gauge theories with 8 supercharges in 3, 4, 5, and 6 dimensions. Inspired by simply laced 3d N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 4 supersymmetric quiver gauge theories, we consider Coulomb branches constructed from non-simply laced quivers with edge multiplicity k and no flavor nodes. In a computation of the Coulomb branch as the space of dressed monopole operators, a center-of-mass U(1) symmetry needs to be ungauged. Typically, for a simply laced theory, all choices of the ungauged U(1) (i.e. all choices of ungauging schemes ) are equivalent and the Coulomb branch is unique. In this note, we study various ungauging schemes and their effect on the resulting Coulomb branch variety. It is shown that, for a non-simply laced quiver, inequivalent ungauging schemes exist which correspond to inequivalent Coulomb branch varieties. Ungauging on any of the long nodes of a non-simply laced quiver yields the same Coulomb branch C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{C} $$\end{document}. For choices of ungauging the U(1) on a short node of rank higher than 1, the GNO dual magnetic lattice deforms anisotropically such that it no longer corresponds to a Lie group, and therefore, the monopole formula yields a non-valid Coulomb branch. However, if the ungauging is performed on a short node of rank 1, the one-dimensional magnetic lattice is rescaled along its single direction i.e. isotropically and the corresponding Coulomb branch is an orbifold of the form C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{C} $$\end{document}/ℤk . Ungauging schemes of 3d Coulomb branches provide a particularly interesting and intuitive description of a subset of actions on the nilpotent orbits studied by Kostant and Brylinski [1]. The ungauging scheme analysis is carried out for minimally unbalanced Cn, affine F4, affine G2, and twisted affine D43\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {D}_4^{(3)} $$\end{document} quivers, respectively. The analysis is complemented with computations of the Highest Weight Generating functions.