发表机构
Università degli Studi di Napoli Federico II; INFN, Sezione di Napoli; Università di Bari; INFN, Sezione di Bari; School of Theoretical Physics Dublin Institute for Advanced Studies（那不勒斯费德里科二世大学; 意大利国家核物理研究所那不勒斯分部; 巴里大学; 意大利国家核物理研究所巴里分部; 都柏林高等研究院理论物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究杨-米尔斯理论从五维到四维的维度约化，提出规范协变Hadamard约化方法，揭示约化理论为杨-米尔斯-希格斯理论，并以U(2)为例分析希格斯机制及费米子质量生成。
AI 中文摘要
我们研究了非阿贝尔杨-米尔斯理论从五维到四维的维度约化。在此框架中，Hadamard约化被表述为对规范等价类的限制，这些等价类在约化方向的平移下（模去规范变换）保持不变。核心结果是，在规范固定之前，约化理论的伴随标量并不是联络分量$A_u$本身，而是规范协变组合$\widetilde{\Phi}=\epsilon-\iota_YA$，它自然地来自协变Cartan恒等式。通常与$A_u$的等同关系，在$u$无关规范中（采用此处约定的符号约定）得以恢复，而整体和乐数据仍需作为额外信息单独指定。我们证明了约化理论采取杨-米尔斯-希格斯理论的形式，其中希格斯场处于伴随表示。作为例子，我们聚焦于$U(2)$规范理论，并分析了当约化理论围绕母理论基态展开时的希格斯机制及相关的对称性破缺模式。随后我们引入费米子，并证明在$u$无关规范中，规范联络的额外维分量产生一个赝标量汤川耦合，在真空构型上，通过手征场重新定义可以将其转化为费米子质量项，而规范相互作用保持矢量性。
英文摘要
We study the dimensional reduction of non-Abelian Yang-Mills theory from five to four dimensions. In this framework, Hadamard descent is formulated as a restriction to gauge-equivalence classes that are invariant, up to gauge transformations, under translations along the reduced direction. The central result is that, prior to gauge fixing, the adjoint scalar of the reduced theory is not the connection component $A_u$ itself, but the gauge-covariant combination $\widetildeΦ=ε-ι_YA$, which follows naturally from the covariant Cartan identity. The usual identification with $A_u$ is recovered, up to the sign convention adopted here, in the $u$-independent gauge, while global holonomy data remain additional information to be specified separately. We show that the reduced theory takes the form of a Yang--Mills--Higgs theory with the Higgs field in the adjoint representation. As an example, we focus on the $U(2)$ gauge theory and analyze the Higgs mechanism, together with the associated symmetry breaking pattern, when the reduced theory is expanded around the ground state of the parent theory. We then include fermions and show that, in the $u$-independent gauge, the extra-dimensional component of the gauge connection generates a pseudoscalar Yukawa coupling which, on the vacuum configuration, can be converted into a fermion mass term by a chiral field redefinition, while the gauge interaction remains vectorial.
Comments16 pages, 1 table
