论文标题
$ \ Mathcal n = 2 $量规理论的同时定位
Cohomological Localization of $\mathcal N = 2$ Gauge Theories with Matter
论文作者
论文摘要
我们在具有杀伤矢量场和孤立的固定点的四维流形上构建了具有延长的超对称性的大型仪表理论。我们将先前的结果限于超级阳米尔斯理论，以$ \ natercal {n} = 2 $仪表理论在内。我们提出了一个一般框架，其中包括唐纳森·威特（Donaldson-Witten）理论和Pestun关于$ S^4 $的理论，作为两种特殊情况。这是通过在同一个学变量中表达字段来实现的，该磁场的特征是由超对称性决定的，并且需要对两种形式的自以为是的普遍概念和旋转器的手性。最后，我们实施本地化技术，以计算我们建立的共同体理论的确切分区功能，并为具有多种拓扑的流形编写明确的结果。
We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $\mathcal{N}=2$ gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun's theory on $S^4$ as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.
