论文标题
a-branes，叶子和本地化
A-branes, foliations and localization
论文作者
论文摘要
本文研究了稳定$ a $ branes的列举不变性的概念，并讨论了其与光谱和指数网络定义的不变性的关系。稳定的$ a $ branes及其计数的自然定义是由拓扑$ a $ model的字符串理论来源提供的。这是单个$ d3 $ brane的超对称量子力学的Witten索引，该指数在Calabi-yau三倍的特殊Lagrangian上支持。从几何上讲，这与$ a $ a-Brane Moduli空间的Euler特性密切相关。使用在此模量空间上的天然圆环动作，我们通过均衡定位将其欧拉特征的计算减少到固定点的计数。在研究与固定点相对应的$ a溴化物时，我们与光谱和指数网络的定义联系。我们发现通过Witten索引定义的计数与网络定义的BPS不变性之间的一致性。从扩展过程中，我们的定义还与$ b $ branes的Donaldson-Thomas不变性匹配。
This paper studies a notion of enumerative invariants for stable $A$-branes, and discusses its relation to invariants defined by spectral and exponential networks. A natural definition of stable $A$-branes and their counts is provided by the string theoretic origin of the topological $A$-model. This is the Witten index of the supersymmetric quantum mechanics of a single $D3$ brane supported on a special Lagrangian in a Calabi-Yau threefold. Geometrically, this is closely related to the Euler characteristic of the $A$-brane moduli space. Using the natural torus action on this moduli space, we reduce the computation of its Euler characteristic to a count of fixed points via equivariant localization. Studying the $A$-branes that correspond to fixed points, we make contact with definitions of spectral and exponential networks. We find agreement between the counts defined via the Witten index, and the BPS invariants defined by networks. By extension, our definition also matches with Donaldson-Thomas invariants of $B$-branes related by homological mirror symmetry.
