Are ZN-Bubbles Really There?
Are ZN-Bubbles Really There?
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ZN-气泡真的存在吗？
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发表时间：
1994
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通讯作者：
A. Smilga
中科院分区：
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作者：
A. Smilga
我们认为，在标准方法中，用Polyakov圈平均值不同来区分的热纯杨-米尔斯理论的不同Z-N热真空实际上对应于同一个物理状态。一个关键的讨论的论点，这通常是提出赞成相反的结论（即，在纯连续杨米尔斯理论，不同的Z N -阶段可能共存于物理空间中，被分隔的域壁与有限的表面能），给出。特别地，我们注意到同样的论证可以同样容易地应用于阿贝尔理论，并将导致高T四维QED中墙的存在和Schwinger模型中质量为π T2/ e的奇异高T孤子的出现。我们强调，这些配置可能与欧几里得路径积分相关，但不对应于真实的闵可夫斯基空间物体。我们还讨论了格点理论，并将其通常的SU（N）形式与涉及伴随矩阵∈ SU（N）/ZN的形式进行了比较。这两个理论应该在连续极限中一致，但后者（与前者相反）没有Z N对称性的痕迹，因此没有任何东西被破坏（这在强耦合极限中特别明显）。最近的数值格子计算的壁面能做得太接近强耦合制度，并没有结论。我们还注意到，π P π T的相位不是一个物理上可测量的量，与去禁闭相变相关的适当序参量不是π P π T，而只是在大距离处的相关器π P（x）P *（0）π T。
Abstract We argue that different Z N thermal vacua of hot pure Yang-Mills theory distinguished in the standard approach by different values of Polyakov loop average 〈P〉 T correspond actually to one and the same physical state. A critical discussion of the arguments, which are usually put forward in favor of the opposite conclusion (that, in pure continuum Yang-Mills theory, distinct Z N -phases may coexist in the physical space, being separated by the domain walls with finite surface energy), is given. In particular, we note that the same arguments can be applied with equal ease to abelian theories and would lead to the existence of the walls in high- T four-dimensional QED and to the appearance of the queer high- T solitons with the mass ∝ T 2 / e in the Schwinger model. We emphasize that these configurations may be relevant for the Euclidean path integral but do not correspond to real Minkowski space objects. We also discuss the lattice theories and confront the usual SU ( N ) version thereof with the version involving adjoint matrices ∈ SU ( N )/ Z N . These two theories should coincide in the continuum limit, but the latter (in contrast to the former) has no trace of Z N -symmetry so that nothing is broken (this is especially clear in the strong coupling limit). The recent numerical lattice calculations of the wall surface energy are done too close to the strong coupling regime and are not conclusive. We note also that the phase of 〈P〉 T is not a physically measurable quantity and that the proper order parameter associated with the deconfinement phase transition is not 〈P〉 T but only the correlator 〈 P ( x ) P *(0)〉 T at large distances.