The monomial-divisor mirror map
The monomial-divisor mirror map
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单项除数镜像映射
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
D. Morrison
中科院分区：
文献类型：
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作者：
P. Aspinwall;B. Greene;D. Morrison
对于环面变体中的每一个Calabi-Yau超曲面族，Batyrev提出了一个可能的镜像伙伴（它也是Calabi-Yau超曲面族）。我们解释了这些超曲面的某些Hodge群之间同构的自然构造，正如镜像对称所预测的那样，我们称之为单因子镜像映射。我们指出这个映射如何被解释为两个Calabi-Yau流形的模空间之间期望镜像同构的微分。我们对镜像同构的形式提出了一个非常精确的猜想，当它与第三位作者之前的一些猜想结合起来时，就会完全说明它。在此基础上，我们得出了以Calabi-Yau空间的不同二元模型为目标的非线性sigma模型的模空间可以通过解析延拓连接起来，进一步的解析延拓可以得到其他类型共形场论的模空间。（最后一个结论是威滕最先提出的。）
For each family of Calabi-Yau hypersurfaces in toric varieties, Batyrev has proposed a possible mirror partner (which is also a family of Calabi-Yau hypersurfaces). We explain a natural construction of the isomorphism between certain Hodge groups of these hypersurfaces, as predicted by mirror symmetry, which we call the monomial-divisor mirror map. We indicate how this map can be interpreted as the differential of the expected mirror isomorphism between the moduli spaces of the two Calabi-Yau manifolds. We formulate a very precise conjecture about the form of that mirror isomorphism, which when combined with some earlier conjectures of the third author would completely specify it. We then conclude that the moduli spaces of the nonlinear sigma models whose targets are the different birational models of a Calabi-Yau space should be connected by analytic continuation, and that further analytic continuation should lead to moduli spaces of other kinds of conformal field theories. (This last conclusion was first drawn by Witten.)