论文标题
$ \ boldsymbol的折衷风味对称性{\ mathbb {z} _2} $ orbifold
The eclectic flavor symmetry of the $\boldsymbol{\mathbb{Z}_2}$ orbifold
论文作者
论文摘要
模块化对称性自然与传统风味对称性和$ \ Mathcal {cp} $相结合，从而产生了所谓的折衷风味对称性。 We apply this scheme to the two-dimensional $\mathbb{Z}_2$ orbifold, which is equipped with two modular symmetries $\mathrm{SL}(2,\mathbb{Z})_T$ and $\mathrm{SL}(2,\mathbb{Z})_U$ associated with two moduli: the Kähler modulus $ t $和复杂的结构模量$ u $。结果有限模块组为$（（S_3 \ times S_3）\ rtimes \ Mathbb {z} _4）\ times \ times \ times \ mathbb {z} _2 $，包括镜像对称（交换$ t $和$ u $）和一般性的$ \ mathcal $ \ mathcal {cp {cp {cp} $ - thromestation。连同传统的风味对称$（D_8 \ times d_8）/\ Mathbb {z} _2 $，这导致了一个具有4608个元素的巨大折衷风味群。在模量空间中的特定区域，我们观察到增强的统一风味对称性，对于四面体形状的Orbifold和$ \ langle t \ rangle = \ langle u \ langle u \ rangle = \ exp（π\，\，\，\ mathrm {i}} \，/\，3）$。这种丰富的折衷结构暗示了粒子物理模型得出的有趣的（模块化）风味组。
Modular symmetries naturally combine with traditional flavor symmetries and $\mathcal{CP}$, giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional $\mathbb{Z}_2$ orbifold, which is equipped with two modular symmetries $\mathrm{SL}(2,\mathbb{Z})_T$ and $\mathrm{SL}(2,\mathbb{Z})_U$ associated with two moduli: the Kähler modulus $T$ and the complex structure modulus $U$. The resulting finite modular group is $((S_3\times S_3)\rtimes \mathbb{Z}_4)\times\mathbb{Z}_2$ including mirror symmetry (that exchanges $T$ and $U$) and a generalized $\mathcal{CP}$-transformation. Together with the traditional flavor symmetry $(D_8\times D_8)/\mathbb{Z}_2$, this leads to a huge eclectic flavor group with 4608 elements. At specific regions in moduli space we observe enhanced unified flavor symmetries with as many as 1152 elements for the tetrahedral shaped orbifold and $\langle T \rangle = \langle U \rangle = \exp(π\,\mathrm{i}\,/\,3)$. This rich eclectic structure implies interesting (modular) flavor groups for particle physics models derived form string theory.
