论文标题
模块化不变风味模型中的对称性和稳定器
Symmetries and stabilisers in modular invariant flavour models
论文作者
论文摘要
模块化不变性的想法提供了一种新颖的风味混合解释。在有限的模块化对称$γ_n$的背景下，对于给定的元素$γ\在γ_n$中，我们提出了一种用于查找稳定器的算法（Moduli Fields $τ_γ$的特定值在与$γ$相关的操作下保持不变，该算法保持不变）。然后，我们使用该算法来找到有限模块化组的每个稳定器，价格为$ n = 2 $至$ 5 $，即$γ_2\ simeq s_3 $，$γ_3\ simeq a_4 $，$γ_4$，$γ_4\ simeq s_4 $和$γ_3$ and $γ_5\ simeq a __ _5 $。然后，这些稳定器保留了$γ_n$的特定环状亚组。这是一种构建费米子混合模型，在该模型中，每个费米子部门都保留了单独的残差对称性。
The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries $Γ_N$ and for a given element $γ\in Γ_N$, we present an algorithm for finding stabilisers (specific values for moduli fields $τ_γ$ which remain unchanged under the action associated to $γ$). We then employ this algorithm to find all stabilisers for each element of finite modular groups for $N=2$ to $5$, namely, $Γ_2\simeq S_3$, $Γ_3\simeq A_4$, $Γ_4\simeq S_4$ and $Γ_5\simeq A_5$. These stabilisers then leave preserved a specific cyclic subgroup of $Γ_N$. This is of interest to build models of fermionic mixing where each fermionic sector preserves a separate residual symmetry.
