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On the equivalence of Batyrev and BHK mirror symmetry constructions
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-12-09 , DOI: 10.1016/j.nuclphysb.2020.115271
Alexander Belavin , Boris Eremin

We consider the connection between two constructions of the mirror partner for the Calabi-Yau orbifold. This orbifold is defined as a quotient by some suitable subgroup G of the phase symmetries of the hypersurface XM in the weighted projective space, cut out by a quasi-homogeneous polynomial WM. The first, Berglund–Hübsch–Krawitz (BHK) construction, uses another weighted projective space and the quotient of a new hypersurface XMT inside it by some dual group GT. In the second, Batyrev construction, the mirror partner is constructed as a hypersurface in the toric variety defined by the reflexive polytope dual to the polytope associated with the original Calabi-Yau orbifold. We give a simple evidence of the equivalence of these two constructions.



中文翻译:

关于巴特列夫和BHK镜像对称构造的等价性

我们考虑卡拉比尤(Calabi-Yau)双向反射镜的两个镜像伙伴结构之间的连接。该曲面被超曲面的相位对称的一些合适的子群G定义为商X中号 在加权射影空间中,由准齐次多项式切出 w ^中号。第一个是Berglund–Hübsch–Krawitz(BHK)结构,它使用了另一个加权射影空间和新超曲面的商X中号Ť 里面有一些双重团体 GŤ。在第二个Batyrev构造中,镜像伙伴被构造为复曲面的超曲面,该曲面由与原始Calabi-Yau双曲面相关联的多面体对折的多面体所定义。我们给出这两种结构的等效性的简单证据。

更新日期:2020-12-09
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