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arXiv 1610.06255hep-th
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$\mathbb{R}\times S^5$上交换M5膜的Witten指标

Witten indices of abelian M5 brane on $\mathbb{R}\times S^5$

Dongsu Bak, Andreas Gustavsson

备注：
48 pages, several clarifications added
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摘要：

在保持超对称性的R规范场背景下，计算了洛仑兹签名的$\mathbb{R}\times S^5$上阿贝尔6d张量和超多重态的Witten指数和配分函数.我们考虑一个通用的超对称挤压，也承认挤压的霍普夫纤维。对欧氏M5膜的Wick旋转相当于挤压参数和超多重态质量参数的Wick旋转。我们分别计算张量和超多重态的Casimir能量，并将其与相应的引力异常多项式相匹配。我们提取Witten指数在$\mathbb{R}\times \mathbb{CP}^2$，并发现这是零，再次匹配的消失异常多项式的奇数维空间。

英文摘要：

Witten indices and partition functions are computed for abelian 6d tensor and hypermultiplets on $\mathbb{R}\times S^5$ in Lorentzian signature in an R gauge field background which preserves some supersymmetry. We consider a generic supersymmetric squashing that also admits squashing of the Hopf fiber. Wick rotation to Euclidean M5 brane amounts to Wick rotation of squashing parameters and the hypermultiplet mass parameter. We compute Casimir energies for tensor and hypermultiplets separately for general squashing, and match these with the corresponding gravitational anomaly polynomials. We extract Witten indices on $\mathbb{R}\times \mathbb{CP}^2$ and find that this is zero, again matching with the vanishing anomaly polynomial on an odd dimensional space.

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