Donaldson-Witten理论的高维类比
高能物理 - 理论
2009-10-30 v2 dg-ga
微分几何
摘要
我们在具有完整性的八维流形上提出了一种Donaldson-Witten型场论。我们证明了应力张量对于保持完整性的度规变分是BRST精确的，并给出了此类变分下的不变量。在六维和七维，我们分别提出了在Calabi-Yau三维流形和完整性流形上的类似理论。我们指出，这些理论通过考虑定义于此类流形上的超对称Yang-Mills理论而得到。这些理论在保持完整性结构的度规变分下不变，而无需twisting。这一陈述是Donaldson-Witten场论在超凯勒4维流形上无需twisting即为拓扑的一个高维类比。Floer上同调的高维类比被简要勾勒。所有这些理论都自然出现在弦论的背景下。
引用
@article{arxiv.hep-th/9705138,
title = {Higher Dimensional Analogues of Donaldson-Witten Theory},
author = {B. S. Acharya and M. O'Loughlin and B. Spence},
journal= {arXiv preprint arXiv:hep-th/9705138},
year = {2009}
}
备注
23 Pages, Latex. Our statement that these theories are independent of the metric is corrected to the statement that the theories are invariant under deformations that preserve the holonomy structure of the manifold. We also include more details of the construction of a higher dimensional analogue of Floer theory. Three references are added