Instantons, quivers and noncommutative Donaldson-Thomas theory
Instantons, quivers and noncommutative Donaldson-Thomas theory
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瞬子、颤振和非交换唐纳森-托马斯理论
DOI：
10.1016/j.nuclphysb.2011.08.002
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发表时间：
2011
影响因子：
2.8
通讯作者：
Cirafici M
中科院分区：
文献类型：
--
作者：
Cirafici M
通过分析瞬子对六维拓扑规范理论的贡献，我们构造了与阿贝尔轨道奇点相关的非对易Donaldson-Thomas不变量。这种规范理论的非对易变形局限于非对易瞬子，这些瞬子可以用三维杨氏图来分类，这些图根据轨道群给盒子着色。我们为这些规范场配置构建了一个模空间，它允许我们通过计算具有关系的规范场的表示来计算其虚数。非对易规范理论的瞬子动力学的编码，并通过广义麦凯对应与奇点的几何相关联。利用拓扑量子力学的方法，在量子力学的基础上实现了计算非对易Donaldson-Thomas不变量的BPS态指数。我们说明了这些建设与几个明确的例子，也涉及更高的秩库仑分支不变量和几何形状与紧凑的因子，并连接我们的方法与其他文献中。
We construct noncommutative Donaldson–Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson–Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.