论文标题
磁带上的模块化风味对称性
Modular Flavor Symmetry on Magnetized Torus
论文作者
论文摘要
我们研究磁性圆环模型中的模块化不变性。模块化不变风味模型是最近提出的用于解决风味拼图的假设，在该拼图中，风味对称性来自模块化不变性。在此框架中，耦合常数（例如Yukawa耦合）也会在风味对称性下进行转换。我们表明，在模块化组的特定亚组下，磁化圆环模型的低能有效理论是不变的。由于Yukawa耦合以及手性零模式在模块化组下变化，因此上述模块化亚组（称为模块化风味对称性）提供了一种新型的模块化不变风味模型，具有$ d_4 \ times \ times \ times \ mathbb {z} _2 _2 _2 $，$ \ Mathbb {Z} _2 $，和$（\ Mathbb {Z} _8 \ Times \ MathBb {Z} _2）\ rtimes \ Mathbb {Z} _2 $。我们还发现，在磁性圆环模型中产生的常规离散风味对称性与模块化风味对称性不合同。结合两个对称性，我们获得了更大的风味对称性，其中传统的风味对称性是整个组的正常亚组。
We study the modular invariance in magnetized torus models. Modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework coupling constants such as Yukawa couplings are also transformed under the flavor symmetry. We show that the low-energy effective theory of magnetized torus models is invariant under a specific subgroup of the modular group. Since Yukawa couplings as well as chiral zero modes transform under the modular group, the above modular subgroup (referred to as modular flavor symmetry) provides a new type of modular invariant flavor models with $D_4 \times \mathbb{Z}_2$, $(\mathbb{Z}_4 \times \mathbb{Z}_2) \rtimes \mathbb{Z}_2$, and $(\mathbb{Z}_8 \times \mathbb{Z}_2) \rtimes \mathbb{Z}_2$. We also find that conventional discrete flavor symmetries which arise in magnetized torus model are non-commutative with the modular flavor symmetry. Combining both two symmetries we obtain a larger flavor symmetry, where the conventional flavor symmetry is a normal subgroup of the whole group.
