$\boldsymbol{\mathbb{Z}_2}$轨道的折衷味对称性
The eclectic flavor symmetry of the $\boldsymbol{\mathbb{Z}_2}$ orbifold
摘要：
模对称性自然地与传统的味对称性和$\mathcal{CP}$相结合，产生了所谓的折衷味对称性。我们应用这个计划的二维$\mathbb{Z}_2$ orbifold，这是配备了两个模块的对称性$\mathrm{SL}(2,\mathbb{Z})_T$和$\mathrm{SL}(2,\mathbb{Z})_U$与两个模块：Kähler模块$T$和复杂的结构模块$U$。得到的有限模群是$((S_3\times S_3)\rtimes \mathbb{Z}_4)\times\mathbb{Z}_2$，它包括镜像对称（交换$T$和$U$）和广义$\mathcal{CP}$ -变换。再加上传统的味道对称性$(D_8\times D_8)/\mathbb{Z}_2$，这导致了一个巨大的折衷主义的味道组与4608个元素。在特定区域的模量空间，我们观察到增强统一的味道对称性与多达1152个元素的四面体形orbifold和$\langle T \rangle = \langle U \rangle = \exp(π\,\mathrm{i}\,/\,3)$。这种丰富的折衷结构意味着有趣的（模块化的）味道群的粒子物理模型来自弦理论。
英文摘要：
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.
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