AI 中文总结
研究在\(SO(3)\)规范理论中构建有限张力非阿贝尔\(A_4\)涡旋解，通过自旋 - 3希格斯场希格斯化。得到显式轴对称解，确定张力并研究其行为，还证明涡旋与\(A_4\)离散规范理论的联系，建立非可逆缺陷的紫外完备。
AI 中文摘要
我们在一个可重整化的\((3 + 1)\)维\(SO(3)\)规范理论中构建了有限张力的非阿贝尔涡旋解，该理论通过一个自旋 - 3表示的希格斯场被希格斯化为四面体群\(A_4\)。由于真空流形是\(SO(3)/A_4\)，涡旋由非阿贝尔基本群\(\pi_1(SO(3)/A_4)\simeq \widetilde{A}_4\)（二元四面体群）表征。我们得到了携带与\(A_4\)的二阶和三阶共轭类相对应的和乐的显式轴对称涡旋解，数值确定了它们的张力，并表明它们根据希格斯和规范玻色子质量比表现出I型、II型和博戈莫尔尼 - 普拉萨德 - 索末菲型行为。涡旋按\(\widetilde{A}_4\)的共轭类分类，其红外描述由\(A_4\)的共轭类标记。我们进一步证明，光滑的有限张力涡旋在红外下简化为\(A_4\)离散规范理论的古科夫 - 维滕表面算符，从而在可重整化规范 - 希格斯理论中建立了非可逆缺陷的有限能量紫外完备。
英文摘要
We construct finite-tension non-Abelian vortex solutions in a renormalizable $(3+1)$-dimensional $SO(3)$ gauge theory Higgsed to the tetrahedral group $A_4$ by a Higgs field in the spin-3 representation. Since the vacuum manifold is $SO(3)/A_4$, the vortices are characterized by the non-Abelian fundamental group $π_1(SO(3)/A_4)\simeq \widetilde{A}_4$, the binary tetrahedral group. We obtain explicit axisymmetric vortex solutions carrying holonomies corresponding to the order-two and order-three conjugacy classes of $A_4$, determine their tensions numerically, and show that they exhibit type-I, type-II, and Bogomol'nyi--Prasad--Sommerfield-like behavior depending on the Higgs and gauge boson mass ratios. The vortices are classified by conjugacy classes of $\widetilde{A}_4$, while their infrared descriptions are labeled by conjugacy classes of $A_4$. We further demonstrate that the smooth finite-tension vortices reduce in the infrared to Gukov--Witten surface operators of the $A_4$ discrete gauge theory, thereby establishing a finite-energy ultraviolet completion of non-invertible defects in a renormalizable gauge-Higgs theory.
Comments14 pages, 4 figures, 2 tables
