摘要翻译：
本文讨论紧致“勉强”$G2$流形的镜像对称性问题，即(cy$乘s^1)/\MathBB{Z}2$形式的$G2$流形。我们提出任何勉强$G_2$流形的镜像是另一勉强流形的镜像，它被构造为CY基的\emph{镜像}的纤维。同时，我们将第一类Joyce流形描述为“勉强”，并证明了所有族的下CY是自镜的，且$h^{1,1}=h^{2,1}=19$。由此我们提出第一类Joyce空间的镜像将是另一类Joyce空间的镜像，并提出在异种/M-理论意义上这个自镜像CY族是K3$乘以S1$的对偶，这是Borcea-Voisin结构的一个特例。由此我们得出结论，在第一类Joyce流形上的11维超重力压缩中不存在5-膜瞬态。
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英文标题：
《Mirror symmetry aspects for compact G_2 manifolds》
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作者：
Sema Salur and Osvaldo Santillan
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：High Energy Physics - Theory        高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Geometric Topology        几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
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英文摘要：
  The present paper deals with mirror symmetry aspects of compact ``barely'' $G_2$ manifolds, that is, $G_2$ manifolds of the form (CY$\times S^1)/\mathbb{Z}_2$. We propose that the mirror of any barely $G_2$ manifold is another barely one and which is constructed as a fibration of the \emph{mirror} of the CY base. Also, we describe the Joyce manifolds of the first kind as ``barely'' and we show that the underlying CY of all the family is self-mirror with $h^{1,1}=h^{2,1}=19$. We thus propose that the mirror of a Joyce space of the first kind will be another Joyce space of the first kind.We also suggest that this self-mirror CY family is dual to K3$\times S^1$ in the heterotic/M-theory sense, and that arise as a particular case of the Borcea-Voisin construction. As a spin-off we conclude from this analysis that no 5-brane instantons are present in compactifications of eleven dimensional supergravity over Joyce manifolds of the first kind.
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PDF链接：
https://arxiv.org/pdf/0707.1356