论文标题
在$ SU（n）$量表理论中的边界条件的表示矩阵上
On representation matrices of boundary conditions in $SU(n)$ gauge theories compactified on two-dimensional orbifolds
论文作者
论文摘要
我们研究了$ su（n）$或$ u（n）$ u（n）$量表理论在Orbifolds $ t^2/{\ Mathbb Z} _n $（$ n = 2，3，4，4，6 $）上的每个等价代表的存在。我们认为该理论具有全局$ g'= u（n）$对称性。使用约束，统一转换和量规变换，我们检查了表示矩阵是否可以同时变为对角线。我们表明，至少有一个对角线代表必须在$ t^2/{\ mathbb z} _2 $和$ t^2/{\ mathbb z} _3 $上，但在$ t^2/{矩阵，但也是非对角线的$ 2 \ times 2 $和非对角线$ 3 \ times 3 $和$ 2 \ times 2 $，作为Block-Diagonal子膜的成员。这些非对角性矩阵具有离散的参数，这意味着降级对称性破坏可能是由离散的Wilson线相引起的。
We study the existence of diagonal representatives in each equivalence class of representation matrices of boundary conditions in $SU(n)$ or $U(n)$ gauge theories compactified on the orbifolds $T^2/{\mathbb Z}_N$ ($N = 2, 3, 4, 6$). We suppose that the theory has a global $G' = U(n)$ symmetry. Using constraints, unitary transformations and gauge transformations, we examine whether the representation matrices can simultaneously become diagonal or not. We show that at least one diagonal representative necessarily exists in each equivalence class on $T^2/{\mathbb Z}_2$ and $T^2/{\mathbb Z}_3$, but the representation matrices on $T^2/{\mathbb Z}_4$ and $T^2/{\mathbb Z}_6$ can contain not only diagonal matrices but also non-diagonal $2 \times 2$ ones and non-diagonal $3 \times 3$ and $2 \times 2$ ones, respectively, as members of block-diagonal submatrices. These non-diagonal matrices have discrete parameters, which means that the rank-reducing symmetry breaking can be caused by the discrete Wilson line phases.
