Geometric singularities and spectra of Landau-Ginzburg models
Geometric singularities and spectra of Landau-Ginzburg models
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Landau-Ginzburg 模型的几何奇点和谱
DOI：
10.1007/bf02102062
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发表时间：
1991
影响因子：
2.4
通讯作者：
S. Yau
中科院分区：
文献类型：
--
作者：
B. Greene;S. Roan;S. Yau
讨论了加权射影空间中超共形弦紧化的一些数学和物理问题。特别是，我们重铸的路径积分参数建立在几何框架中的朗道-金兹伯格共形理论和卡-丘弦紧化之间的联系。然后，我们证明了一个完整的交叉（从光滑的情况下通过）的第一陈类消失的朴素表达式是足够的，以确保所得到的品种，这是一般奇异的，可以解决到一个光滑的卡-丘空间。这证明了最近在朗道-金兹伯格模型的研究中所做的大量分析是正确的。此外，我们推导出一些简单的公式，用于确定这些理论中的维滕指数是互补的，使用半经典推理Vafa。最后，我们还评论了非正规双折叠Landau-Ginzburg理论的可能几何意义。
Some mathematical and physical aspects of superconformal string compactification in weighted projective space are discussed. In particular, we recast the path integral argument establishing the connection between Landau-Ginzburg conformal theories and Calabi-Yau string compactification in a geometric framework. We then prove that the naive expression for the vanishing of the first Chern class for a complete intersection (adopted from the smooth case) is sufficient to ensure that the resulting variety, which is generically singular, can be resolved to a smooth Calabi-Yau space. This justifies much analysis which has recently been expended on the study of Landau-Ginzburg models. Furthermore, we derive some simple formulae for the determination of the Witten index in these theories which are complimentary to those derived using semiclassical reasoning by Vafa. Finally, we also comment on the possible geometrical significance ofunorbifolded Landau-Ginzburg theories.