N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model
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DOI：
10.1007/jhep08(2017)090
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发表时间：
2017-07
影响因子：
5.4
通讯作者：
Cyril Closset;Hee-Cheol Kim;Brian Willett
中科院分区：
文献类型：
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作者：
Cyril Closset;Hee-Cheol Kim;Brian Willett
我们计算= 1 超对称规范理论的超对称配分函数，其 R 对称性是在属 g 黎曼曲面 Σ g 上的 p 次主椭圆纤维束。等效地，我们计算广义超对称指数，其中超对称三流形作为空间切片。圆三球面上的普通=1超对称指数被恢复为特例。我们从基于 Σ g 的阿贝尔化规范场的拓扑 A 模型的角度来进行此计算。该 A 模型（或 A 扭曲二维=(2, 2) 规范理论）编码了有关广义指数的所有信息，这些信息被视为包裹在 Σ g× T 2 内 T 2 上的一些规范定义的表面缺陷的期望值。通过环面的紧致化定义，A 模型还具有受四维’t Hooft 异常控制的自然模属性。作为我们结果的应用，我们提供了塞伯格对偶性的新测试。我们还提出了一个新的三球指数评估公式，作为二维真空的总和。
We compute the supersymmetric partition function of= 1 supersymmetric gauge theories with an R-symmetry on, a principal elliptic fiber bundle of degree p over a genus-g Riemann surface, Σ g. Equivalently, we compute the generalized supersymmetric index, with the supersymmetric three-manifoldas the spatial slice. The ordinary= 1 supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological A-model for the abelianized gauge fields on the base Σ g. This A-model—or A-twisted two-dimensional=(2, 2) gauge theory—encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on T 2 inside Σ g× T 2. Being defined by compactification on the torus, the A-model also enjoys natural modular properties, governed by the four-dimensional’t Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.