标题： 模块对称味模型的景观 显示英文标题

标题： Landscape of Modular Symmetric Flavor Models

摘要： 我们从模态味对称性的角度研究模态稳定化。 我们系统地分析了可能的通量紧致化配置中的稳定模态值，研究模态值的概率，并表明哪些模态值在我们的模态稳定化中是有利的。 然后，我们检查它们对模态对称味模型的影响。 发现决定味结构的复结构模态 $\tau$ 的分布集中在具有剩余 $\mathbb{Z}_3$ 对称性的 $SL(2,\mathbb{Z})$ 基本区域的固定点上。 此外，它们也集中在其他特定点上，例如 $|\tau|^2=k/2$ 和 ${\rm Re}\,\tau=0,\pm 1/4, \pm1/2$ 的交点，尽管它们的概率小于 $\mathbb{Z}_3$ 固定点。 一般来说， 复结构模态中的CP破坏真空在弦景观中在统计上不被青睐。 在CP破坏的真空中，特别是当轴子-膨胀子$S$稳定在${\rm Re}\,S=\pm 1/4$时，${\rm Re}\,\tau=\pm 1/4$的值最为有利。 这表明了来自弦模的CP相之间存在强烈的关联。 显示英文摘要

摘要： We study the moduli stabilization from the viewpoint of modular flavor symmetries. We systematically analyze stabilized moduli values in possible configurations of flux compactifications, investigating probabilities of moduli values and showing which moduli values are favorable from our moduli stabilization. Then, we examine their implications on modular symmetric flavor models. It is found that distributions of complex structure modulus $\tau$ determining the flavor structure are clustered at a fixed point with the residual $\mathbb{Z}_3$ symmetry in the $SL(2,\mathbb{Z})$ fundamental region. Also, they are clustered at other specific points such as intersecting points between $|\tau|^2=k/2$ and ${\rm Re}\,\tau=0,\pm 1/4, \pm1/2$, although their probabilities are less than the $\mathbb{Z}_3$ fixed point. In general, CP-breaking vacua in the complex structure modulus are statistically disfavored in the string landscape. Among CP-breaking vacua, the values ${\rm Re}\,\tau=\pm 1/4$ are most favorable in particular when the axio-dilaton $S$ is stabilized at ${\rm Re}\,S=\pm 1/4$. That shows a strong correlation between CP phases originated from string moduli.