论文标题
非磨牙箭筒理论的拆开计划和库仑分支
Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver Theories
论文作者
论文摘要
三维库仑分支在研究超对称规格理论的模量空间中起着重要作用，$ 8 $ $ 8 $以$ 3,4,5 $和$ 6 $尺寸。灵感来自简单的$ 3 $ D $ \ MATHCAL {n} = 4 $超对称颤抖仪的理论，我们认为由具有边缘多重性$ k $的非微薄式砂纸构建的库仑分支，没有风味。在计算库仑分支作为衣服单极操作员的空间中，需要对质量中心$ u（1）$对称性。通常，对于简单的理论，Ungaig $ u（1）$的所有选择（即，Ungauging方案的所有选择）都是等效的，而Coulomb分支是独一无二的。在本说明中，我们研究了各种提高计划及其对所得库仑分支品种的影响。结果表明，对于非简单的箭袋，存在不相等的未钉计划，与不相等的库仑分支品种相对应。在非简单系带箭筒的任何长节点上取消签名都会产生相同的库仑分支$ \ MATHCAL {C} $。对于在高于$ 1 $的短节点上取消$ u（1）$的选择，GNO双磁晶格变形，使其不再对应于Lie组，因此，单极公式产生了非valid colomb分支。但是，如果将Ungaig在等级$ 1 $的短节点上执行，则一维磁晶格沿其单个方向进行固结重新固定，相应的库仑分支是$ \ Mathcal {C}/\ Mathbb {Z} {Z} _K $的形式的Orbifold。 $ 3 $ d库仑分支机构的提高计划提供了一个特别有趣且直观的描述，描述了Kostant和Brylinski Arxiv研究的Nilpotent Orbits的一部分动作：Math/9204227。对最小不平衡的$ C_N $，Aggine $ f_4 $，affine $ g_2 $和扭曲的仿射$ d_4^{（3）} $ Quivers进行了Ungaig计划分析。
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 $3$d $\mathcal{N}=4$ 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 $\mathcal{C}$. For choices of ungauging the $U(1)$ on a short node of rank higher than $1$, the GNO dual magnetic lattice deforms 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 conformally along its single direction and the corresponding Coulomb branch is an orbifold of the form $\mathcal{C}/\mathbb{Z}_k$. Ungauging schemes of $3$d Coulomb branches provide a particularly interesting and intuitive description of a subset of actions on the nilpotent orbits studied by Kostant and Brylinski arXiv:math/9204227. The ungauging scheme analysis is carried out for minimally unbalanced $C_n$, affine $F_4$, affine $G_2$, and twisted affine $D_4^{(3)}$ quivers, respectively.
