The Refined BPS Index from Stable Pair Invariants
The Refined BPS Index from Stable Pair Invariants
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DOI：
10.1007/s00220-014-1978-0
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发表时间：
2012-10
影响因子：
2.4
通讯作者：
Jinwon Choi;S. Katz;A. Klemm
中科院分区：
文献类型：
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作者：
Jinwon Choi;S. Katz;A. Klemm
基于一个关于稳定对模空间上的作用或Nekrasov和Okounkov的等变指标的虚Bialynicki-Birula分解，引入了非紧Calabi-Yau空间上Pandharipande和Thomas的稳定对不变量的改进。这有效地计算了在这些Calabi-Yau几何上减少的精炼索引形式理论。基于物理期望，我们提出了一个精炼不变量的积公式，扩展了Morrison， Mozgovoy， Nagao和Szendroi的局部动机积公式。我们显式地计算了局部和局部的低次精炼不变量，并检验了它们与广义全纯异常直接积分的预测和与乘积公式的一致。在直接积分方法中得到的表达式的模块性允许我们将适当几何上精炼PT不变量的生成函数与Nekrasov的配分函数和透镜空间上chen - simons理论的精炼联系起来。我们也把乘积公式与过墙联系起来。
A refinement of the stable pair invariants of Pandharipande and Thomas for non-compact Calabi–Yau spaces is introduced based on a virtual Bialynicki-Birula decomposition with respect to aaction on the stable pair moduli space, or alternatively the equivariant index of Nekrasov and Okounkov. This effectively calculates the refined index forM-theory reduced on these Calabi–Yau geometries. Based on physical expectations we propose a product formula for the refined invariants extending the motivic product formula of Morrison, Mozgovoy, Nagao, and Szendroi for local. We explicitly compute refined invariants in low degree for localand localand check that they agree with the predictions of the direct integration of the generalized holomorphic anomaly and with the product formula. The modularity of the expressions obtained in the direct integration approach allows us to relate the generating function of refined PT invariants on appropriate geometries to Nekrasov’s partition function and a refinement of Chern–Simons theory on a lens space. We also relate our product formula to wall crossing.