Flavor structure in F-theory compactifications
Flavor structure in F-theory compactifications
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DOI：
10.1007/jhep08(2010)036
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发表时间：
2009-10
影响因子：
5.4
通讯作者：
Hirotaka Hayashi;T. Kawano;Y. Tsuchiya;T. Watari
中科院分区：
文献类型：
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作者：
Hirotaka Hayashi;T. Kawano;Y. Tsuchiya;T. Watari
F-理论是弦理论中容纳超对称大统一的框架之一，所有右手中微子的Yukawa耦合和Majorana质量都在F-理论中产生。带电费米子的汤川耦合产生于余维3奇点，并且已知来自给定奇点的贡献近似为秩1。因此，一般F-理论紧化的低能有效理论中的Yukawa矩阵的近似秩是代数Ngen = 3或某些类型的奇点数中的最小值.如果在SU（5）规范场的整个7-膜上存在一个只有一个E6型点和一个D 6型点的几何，那么在这样的几何上紧化的F-理论将近似地再现真实的世界中的秩-1汤川矩阵.然而，我们发现并不存在这样的几何学。因此，如何在F-理论紧化中生成分层Yukawa特征值是一个问题。到目前为止，文献中的解决方案是采取适当的因式分解极限。在这篇文章中，我们提出了一个替代的解决方案的层次结构的问题（这需要调整一些参数），通过研究如何零模式波函数依赖于复杂的结构模量。在这个解中，我们预言N gen× N gen CKM矩阵只有N gen阶单位元，而不需要额外的参数调整，并且预言轻子混合矩阵将呈现轻子味无政府状态.下型和带电轻子扇区的Yukawa本征值之间的层次结构被预测为小于上型扇区的Yukawa本征值，并且通过跷跷板机制产生的左手中微子的Majorana质量具有小的层次结构。所有这些预测都与我们在真实的世界中观察到的一致。我们还得到了E6型奇点附近的零模波函数的精确描述，其中上型Yukawa耦合产生。
F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of righthanded neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations N gen= 3 or the number of singularity points of certain types. If there is a geometry with only one E 6 type point and one D 6 type point over the entire 7-brane for SU (5) gauge fields, F-theory compactified on such a geometry would reproduce approximately rank-1 Yukawa matrices in the real world. We found, however, that there is no such geometry. Thus, it is a problem how to generate hierarchical Yukawa eigenvalues in F-theory compactifications. A solution in the literature so far is to take an appropriate factorization limit. In this article, we propose an alternative solution to the hierarchical structure problem (which requires to tune some parameters) by studying how zero mode wavefunctions depend on complex structure moduli. In this solution, the N gen× N gen CKM matrix is predicted to have only N gen entries of order unity without an extra tuning of parameters, and the lepton flavor anarchy is predicted for the lepton mixing matrix. The hierarchy among the Yukawa eigenvalues of the down-type and charged lepton sector is predicted to be smaller than that of the up-type sector, and the Majorana masses of left-handed neutrinos generated through the see-saw mechanism have small hierarchy. All of these predictions agree with what we observe in the real world. We also obtained a precise description of zero mode wavefunctions near the E 6 type singularity points, where the up-type Yukawa couplings are generated.