发表机构
Nara Women’s University; Nara University of Education（奈良女子大学; 奈良教育大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出广义离散规范化框架，通过投影特征标推导非阿贝尔群下的不可逆选择规则，限制相互作用并给出耦合关系，以Δ(54)和S₄为例验证。
AI 中文摘要
我们研究了源于具有底层离散全局对称群 $G$ 的理论的离散 $H$-规范化的不可逆选择规则。为了系统地描述这些理论，我们制定了一个包含广义场变换的 $H$-规范化模型的一般框架。我们的方法自然地容纳了非阿贝尔群，其中多维不可约表示起着至关重要的作用。在具有非阿贝尔群的此类模型中，由 $H$ 诱导的变换非平凡地混合了 $G$-多重态的内部分量，可能投影出特定的自由度。因此，基于标准张量积分解或共轭类的传统选择规则变得不足。通过分析完整的半直积 $G \rtimes H$，我们引入了投影特征标来推导非零 $n$-点裸耦合的充分必要条件。此外，我们证明了剩余的场分量遵循一个由它们的 Clebsch-Gordan 系数控制的类融合代数。在现象学上，这些选择规则限制了允许的相互作用，并对耦合常数施加了特定的关系。我们通过具体例子说明了我们的结果，包括 $\Delta(54) \cong \Delta(27)\rtimes \mathbb{Z}_2$ 和 $S_4 \cong A_4 \rtimes \mathbb{Z}_2$。
英文摘要
We investigate non-invertible selection rules originating from the discrete $H$-gauging of theories with an underlying discrete global symmetry group $G$. To systematically describe these theories, we formulate a general framework for $H$-gauged models that incorporates generalized field transformations. Our approach naturally accommodates non-Abelian groups, for which multidimensional irreducible representations play an essential role. In such models with non-Abelian groups, the transformations induced by $H$ non-trivially mix the internal components of $G$-multiplets, potentially projecting out specific degrees of freedom. Consequently, conventional selection rules based on standard tensor product decompositions or conjugacy classes become insufficient. By analyzing the full semidirect product $G \rtimes H$, we introduce projected characters to derive necessary and sufficient conditions for non-vanishing $n$-point bare couplings. Furthermore, we demonstrate that the remaining field components obey an associative fusion-like algebra governed by their Clebsch-Gordan coefficients. Phenomenologically, these selection rules restrict allowed interactions and impose specific relations among coupling constants. We illustrate our results through concrete examples, including $Δ(54) \cong Δ(27)\rtimes \mathbb{Z}_2$ and $S_4 \cong A_4 \rtimes \mathbb{Z}_2$.
Comments41 pages, v2: minor corrections and updated references
