论文标题
pure-higgs从lefschetz-sommese定理中陈述
Pure-Higgs states from the Lefschetz-Sommese theorem
论文作者
论文摘要
我们考虑了在II型calabi-yau压缩中D4D0麸皮的BPS状态和相应的4维黑洞中的BPS状态中相关的N = 4 Quiver量子力学。除了任意数量的非亚洲节点外，这些震颤还具有两个Abelian节点，并满足了一组箭头的一些简单但严格的条件，特别是始终存在封闭的定向环。希格斯分支可以描述为矢量束的一部分的消失基因座，上面有许多格拉曼尼亚人的投射空间的产物。然后，Lefschetz-Sommese定理允许将诱导的诱导的奇异共同体分离，从而导致纯粹态态的概念。我们计算索引计算这些纯粹的纯正状态的索引的明确公式，并证明 - 对于这种特殊的纪念物 - 关于它们的一些先前陈述的猜想。
We consider a special class of N=4 quiver quantum mechanics relevant in the description of BPS states of D4D0 branes in type II Calabi-Yau compactifications and the corresponding 4-dimensional black holes. These quivers have two abelian nodes in addition to an arbitrary number of non-abelian nodes and satisfy some simple but stringent conditions on the set of arrows, in particular closed oriented loops are always present. The Higgs branch can be described as the vanishing locus of a section of a vector bundle over a product of a projective space with a number of Grassmannians. The Lefschetz-Sommese theorem then allows to separate induced from singular cohomology which leads to the notion of pure-Higgs states. We compute explicit formulae for an index counting these pure-Higgs states and prove -- for this special class of quivers -- some previously stated conjectures about them.
