标题： 颜色禁闭与随机矩阵 —— 朝着卡西米尔标度的群流形随机漫步 —— 显示英文标题

标题： Color Confinement and Random Matrices -- A random walk down group manifold toward Casimir scaling --

摘要： 我们解释了在一般约束规范理论中线性约束势与卡西米尔缩放的微观起源。 在约束规范理论如QCD的低温区域，马约拉克线路相对于逆温度是缓慢变化的哈尔随机，除了指数小的修正，这一点由其中一位作者（M.~H.）和若山已经证明。 在精确的哈尔随机性下，马约拉克环的两点关联函数的计算简化为群流形上的随机游走问题。 除了短距离外，具有近似卡西米尔缩放的线性约束势自然地从缓慢变化的哈尔随机性中得出。 在哈尔随机性的指数小修正下，长距离处的弦断裂和卡西米尔缩放的丧失随之出现。 因此，我们得到了仅在中间距离成立的近似卡西米尔缩放，这正是解释格点模拟结果所需要的。 对于$(1+1)$维度的理论，存在一种简化，使得在短距离处也能出现卡西米尔缩放。 显示英文摘要

摘要： We explain the microscopic origin of linear confinement potential with the Casimir scaling in generic confining gauge theories. In the low-temperature regime of confining gauge theories such as QCD, Polyakov lines are slowly varying Haar random modulo exponentially small corrections with respect to the inverse temperature, as shown by one of the authors (M.~H.) and Watanabe. With exact Haar randomness, computation of the two-point correlator of Polyakov loops reduces to the problem of random walk on group manifold. Linear confinement potential with approximate Casimir scaling except at short distances follows naturally from slowly varying Haar randomness. With exponentially small corrections to Haar randomness, string breaking and loss of Casimir scaling at long distance follow. Hence we obtain the Casimir scaling which is only approximate and holds only at intermediate distance, which is precisely needed to explain the results of lattice simulations. For $(1+1)$-dimensional theories, there is a simplification that admits the Casimir scaling at short distances as well.