中心对称和面积定律
Center symmetry and area laws
摘要：
包含物质场的SU（$N_c$）规范理论在$\mathbb{Z}_{N_c}$中心的某个子群的变换下可能是不变的;最大的子群是$\mathbb{Z}_{p}$，$p$依赖于$N_c$和理论中各种物质场的表示。在3+1或2+1时空维中的SU（$N_c$）规范理论，以及任何表象中的物质场，对于表象$R$都有弦张力，由$σ_R =σ_f \, \, \frac{p_R (p-p_R) \, \, g\left (p_R (p-p_R) \right )}{(p-1) \, \, g(p -1 )} $ with $p_R={n_R \, \rm mod}(p)$给出，其中$σ_f $是基本表象的弦张力，$g$是正有限函数，$n_R$是$R$的n阶数。这意味着在这个类中的理论有面积定律的必要条件是理论在中心的非平凡子群下的不变性。值得注意的是，这些结果取决于$p$，而与$N_c$的值无关。
英文摘要：
SU($N_c$) gauge theories containing matter fields may be invariant under transformations of some subgroup of the $\mathbb{Z}_{N_c}$ center; the maximum such subgroup is $\mathbb{Z}_{p}$, with $p$ depending on $N_c$ and the representations of the various matter fields in the theory. Confining SU($N_c$) gauge theories in either 3+1 or 2+1 space-time dimensions and with matter fields in any representation have string tensions for representation $R$ given by $σ_R =σ_f \, \, \frac{p_R (p-p_R) \, \, g\left (p_R (p-p_R) \right )}{(p-1) \, \, g(p -1 )} $ with $p_R={n_R \, \rm mod}(p)$, where $σ_f $ is the string tension for the fundamental representation, $g$ is a positive finite function and $n_R$ is the n-ality of $R$. This implies that a necessary condition for a theory in this class to have an area law is invariance of the theory under a nontrivial subgroup of the center. Significantly, these results depend on $p$ regardless of the value of $N_c$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
