On discrete symmetries and torsion homology in F-theory
On discrete symmetries and torsion homology in F-theory
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F理论中的离散对称性和扭转同调性
DOI：
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
T. Weigand
中科院分区：
文献类型：
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作者：
C. Mayrhofer;Eran Palti;Oskar Till;T. Weigand
研究了f -理论紧化中的离散规范对称与相关Calabi-Yau流形上的扭转同调的关系。关注一个最简单的例子$$ {\mathbb{Z}}_2 $$ 对称，我们展示了有两种物理上不同的方式可以产生这种离散规范对称。首先，m理论在Calabi-Yau三折上的紧化，其支持双截面的属一振动，已知是对偶到具有一个2的六维f理论真空$$ {\mathbb{Z}}_2 $$ 规范对称。我们证明了所得到的五维理论不具有一个2$$ {\mathbb{Z}}_2 $$ 对称，但后者只出现在f理论的去核化极限。因此，第一属纤维的Calabi-Yau流形在同源性中不表现出扭转。与双截面纤维化相关联的是支撑截面的雅可比纤维化。在这些相关但不同的变种上的紧化确实导致了一个2$$ {\mathbb{Z}}_2 $$ 在五维对称，因此，我们明确地发现一个相关的扭转循环。我们用包裹的M2和M5膜确定了离散对称的预期粒子和膜系统，并根据六维理论的圆约简给出了两种情况下的物理场论描述。我们的结果和方法直接推广到更大的离散对称和四维紧化。
A bstractWe study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a ℤ2$$ {\mathbb{Z}}_2 $$ symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a ℤ2$$ {\mathbb{Z}}_2 $$ gauge symmetry. We show that the resulting five-dimensional theories do not have a ℤ2$$ {\mathbb{Z}}_2 $$ symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit torsion in homology. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a ℤ2$$ {\mathbb{Z}}_2 $$ symmetry in five dimensions and, accordingly, we find explicitly an associated torsion cycle. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.
一属纤维振动的 F 理论
影响因子：
5.4
作者：
Braun V
通讯作者：
Braun V
全局 F 理论 GUT 中的阿贝尔规范对称性和质子衰变
影响因子：
5
作者：
T. W. Grimm;T. Weigand
通讯作者：
T. Weigand
四维 F 理论紧化中 Higgsing 的离散规范对称性
影响因子：
5.4
作者：
Mayrhofer;Weigand
通讯作者：
Weigand