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arXiv 1603.09323hep-thmath-phmath.DGmath.MP
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弦论中Calabi-Yau二重流形和非Kahler流形上的$T^4$纤维化

$T^4$ fibrations over Calabi-Yau two-folds and non-Kahler manifolds in string theory

Hai Lin

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22 pages
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摘要：

我们构造了一个八维流形的几何模型，并在II型弦论的背景下实现了它们。这些八维流形是由Calabi-Yau二重上的非平凡$T^{4}$纤维化构造的。这就产生了具有$SU(4)$结构的八维非Kahler Hermitian流形。八维流形也是七维$G_{2}$流形上的一个具有斜挠的圆纤维化。这种类型的八流形在具有$F_{7}$和$F_{3}$通量的IIB型弦论中表现为具有$SU(4)$结构的内部流形。这些流形在通量的存在下具有广义校准周期。

英文摘要：

We construct a geometric model of eight-dimensional manifolds and realize them in the context of type II string theory. These eight-manifolds are constructed by non-trivial $T^{4}$ fibrations over Calabi-Yau two-folds. These give rise to eight-dimensional non-Kahler Hermitian manifolds with $SU(4)$ structure. The eight-manifold is also a circle fibration over a seven-dimensional $G_{2}$ manifold with skew torsion. The eight-manifolds of this type appear as internal manifolds with $SU(4)$ structure in type IIB string theory with $F_{3}$ and $F_{7}$ fluxes. These manifolds have generalized calibrated cycles in the presence of fluxes.

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