arXiv 1012.58072010-12-28hep-thmath.AG

Calabi-Yau族中的弦模相位

String Modular Phases in Calabi-Yau Families

Shabnam Kadir, Monika Lynker, Rolf Schimmrigk

备注：: 34 pages
发表信息：: J.Geom.Phys.61:2453-2469,2011
DOI：: 10.1016/j.geomphys.2011.04.010

摘要：

研究了含有Brieskorn-Pham点的模空间中奇异Calabi-Yau簇的结构.我们的主要工具是在参数空间上构造变形动机族。我们分析这些动机一般纤维和明确计算的$L-$系列奇异纤维的几个家庭。我们发现，由此产生的动机$L-$功能同意与$L-$系列的模块形式，其重量取决于排名的动机和退化的程度的品种。令人惊讶的是，这些motivic $L-$功能是相同的，在几种情况下，$L-$系列来自加权费马超曲面。这表明非锥型的奇异卡-丘空间可以接受弦世界片解释，很像有理理论，而相应的无理共形场论继承了该族加权费马纤维的盖普纳共形场论的信息。这些结果表明，相变通过非conifold配置是物理上合理的。在严重退化的情况下，我们发现动机的维度转变。这进一步表明，具有非锥状奇点的奇异构型可能有助于不同维度的卡-丘变体之间的过渡。

英文摘要：

We investigate the structure of singular Calabi-Yau varieties in moduli spaces that contain a Brieskorn-Pham point. Our main tool is a construction of families of deformed motives over the parameter space. We analyze these motives for general fibers and explicitly compute the $L-$series for singular fibers for several families. We find that the resulting motivic $L-$functions agree with the $L-$series of modular forms whose weight depends both on the rank of the motive and the degree of the degeneration of the variety. Surprisingly, these motivic $L-$functions are identical in several cases to $L-$series derived from weighted Fermat hypersurfaces. This shows that singular Calabi-Yau spaces of non-conifold type can admit a string worldsheet interpretation, much like rational theories, and that the corresponding irrational conformal field theories inherit information from the Gepner conformal field theory of the weighted Fermat fiber of the family. These results suggest that phase transitions via non-conifold configurations are physically plausible. In the case of severe degenerations we find a dimensional transmutation of the motives. This suggests further that singular configurations with non-conifold singularities may facilitate transitions between Calabi-Yau varieties of different dimensions.

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