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arXiv 1702.08424hep-thhep-ph
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单回路的变形、模量稳定性和应变计耦合

Deformations, Moduli Stabilisation and Gauge Couplings at One-Loop

Gabriele Honecker, Isabel Koltermann, Wieland Staessens

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1+84 pages, 16 figures, 32 tables
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摘要：

本文研究了离散挠率下的环面轨道$T^6/(\mathbb{Z}_2\times\mathbb{Z}_6)$上的$\mathbb{Z}_2$轨道奇点的变形，在IIA型定向折叠模型的框架下，用相交的D 6-膜包裹特殊的拉格朗日环.为此，我们采用超曲面形式主义先前开发的orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$离散扭转和适应它的$\mathbb{Z}_2\times\mathbb{Z}_6\timesΩ\mathcal{R}$点群通过modding出剩余的$\mathbb{Z}_3$次对称和orientifold投影$Ω\mathcal{R}$。我们首先研究了局部行为的$\mathbb{Z}_3\timesΩ\mathcal{R}$不变变形轨道下的非零变形，然后开发的方法来评估的分数三周期体积的变形效果的全球。我们证实了支持USp（2N）或SO（2N）规范群的D 6-膜不约束任何形变，而与被具有U（N）规范群的D 6-膜包裹的圈相关的形变参数受到D项超对称破缺的约束。这些特征在arXiv：1509.00048和arXiv：1409.1236中首次构建的全球原型MSSM，左右对称和Pati-Salam模型中暴露出来，我们在这里计算稳定模量的数量并研究改变一些规范耦合值的平坦方向。最后，我们面对的行为下的非零变形沿平面方向与单圈规范阈值校正的orbifold点的三级规范耦合，并讨论了唯象的影响，特别是对可能的大体积的情况下，相应的值的弦尺度$M_{\text{string}}$，为相同的全球D 6膜模型。

英文摘要：

We investigate deformations of $\mathbb{Z}_2$ orbifold singularities on the toroidal orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_6)$ with discrete torsion in the framework of Type IIA orientifold model building with intersecting D6-branes wrapping special Lagrangian cycles. To this aim, we employ the hypersurface formalism developed previously for the orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$ with discrete torsion and adapt it to the $\mathbb{Z}_2\times\mathbb{Z}_6\timesΩ\mathcal{R}$ point group by modding out the remaining $\mathbb{Z}_3$ subsymmetry and the orientifold projection $Ω\mathcal{R}$. We first study the local behaviour of the $\mathbb{Z}_3\timesΩ\mathcal{R}$ invariant deformation orbits under non-zero deformation and then develop methods to assess the deformation effects on the fractional three-cycle volumes globally. We confirm that D6-branes supporting USp(2N) or SO(2N) gauge groups do not constrain any deformation, while deformation parameters associated to cycles wrapped by D6-branes with U(N) gauge groups are constrained by D-term supersymmetry breaking. These features are exposed in global prototype MSSM, Left-Right symmetric and Pati-Salam models first constructed in arXiv:1509.00048 and arXiv:1409.1236, for which we here count the number of stabilised moduli and study flat directions changing the values of some gauge couplings. Finally, we confront the behaviour of tree-level gauge couplings under non-vanishing deformations along flat directions with the one-loop gauge threshold corrections at the orbifold point and discuss phenomenological implications, in particular on possible LARGE volume scenarios and the corresponding value of the string scale $M_{\text{string}}$, for the same global D6-brane models.

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