论文标题
二维晶格标量染色体动力学的通用低温行为
Universal low-temperature behavior of two-dimensional lattice scalar chromodynamics
论文作者
论文摘要
我们研究了具有多组分标量字段的二维晶格理论中全球和本地非亚伯对称性的作用。我们从最大的O（$ m $）开始 - 对称的多组分标量模型，其对称性是部分测量的，以获得SU（$ n_c $）仪表理论（标量镀铬动力学），并带有全局u $（n_f）$（$ n_c \ ge 3 $）或sp（$ n_f $ n_f $ n $ n $ n $ n_c = 2 $ n_c = 2 $ n_c = 2 $ n_c = 2 $ n_c = 2 $ n_c = 22口味。相应地，这些字段属于coset $ s^m $/su（$ n_c $），其中$ s^m $是$ m $ dimensional sphere，$ m = 2 n_f n_f n_c $。与Mermin-Wagner定理一致，该系统总是在有限温度下无序，而临界行为仅在零温度的极限下形成。它的通用特征通过数值有限尺寸缩放方法研究。结果表明，渐近低温行为属于$ n_c> 2 $的2D CP $^{N_F-1} $ field Theory的通用类别，以及2D SP（$ n_f $）for $ n_c = 2 $的2d SP（$ N_F $）理论。这些通用类别对应于与$ n_c = 2 $的SP（$ n_f $）转换下的对称空间相关的2D统计字段理论，并在$ n_c>> 2 $下进行$ n_c = 2 $（$ n_f $）。这些对称组是标量染色体动力学的不变性组，除了$ n_f \ ge n_c> 2 $存在的u（1）风味对称性，这在确定模型的渐近行为方面没有任何作用。
We study the role that global and local nonabelian symmetries play in two-dimensional lattice gauge theories with multicomponent scalar fields. We start from a maximally O($M$)-symmetric multicomponent scalar model, Its symmetry is partially gauged to obtain an SU($N_c$) gauge theory (scalar chromodynamics) with global U$(N_f)$ (for $N_c\ge 3$) or Sp($N_f$) symmetry (for $N_c=2$), where $N_f>1$ is the number of flavors. Correspondingly, the fields belong to the coset $S^M$/SU($N_c$) where $S^M$ is the $M$-dimensional sphere and $M=2 N_f N_c$. In agreement with the Mermin-Wagner theorem, the system is always disordered at finite temperature and a critical behavior only develops in the zero-temperature limit. Its universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the 2D CP$^{N_f-1}$ field theory for $N_c>2$, and to that of the 2D Sp($N_f$) field theory for $N_c=2$. These universality classes correspond to 2D statistical field theories associated with symmetric spaces that are invariant under Sp($N_f$) transformations for $N_c=2$ and under SU($N_f$) for $N_c > 2$. These symmetry groups are the same invariance groups of scalar chromodynamics, apart from a U(1) flavor symmetry that is present for $N_f \ge N_c > 2$, which does not play any role in determining the asymptotic behavior of the model.
