AI 中文总结
本文综述了热QCD中轴向$U(1)$对称性破缺的机制，通过拓扑与格点计算探讨其对手征相变临界行为的影响。
AI 中文摘要
加热物质可以恢复在低温下自发破缺的对称性。量子色动力学（QCD）的轴向$U(1)$对称性则不同：它在具有无质量夸克的经典理论中存在，但通过轴向反常在量子化时被破坏。反常在每个温度下持续存在，但其可观测效应可能减弱。然而，热物质能否在长距离上表现得如同该对称性已恢复？这种有效轴向$U(1)$恢复是否发生，取决于微观夸克和胶子动力学如何控制轴向破缺的强度和空间范围。本综述汇集了理论发展和第一性原理格点QCD计算。我们考察了胶子场拓扑如何塑造低 lying 狄拉克模式及其关联，这些模式如何在不同空间尺度上对轴向破缺作出贡献，以及当夸克质量趋近于零时，这对手征相变的序和临界行为意味着什么。
英文摘要
Heating matter can restore symmetries spontaneously broken at low temperature. The axial $U(1)$ symmetry of quantum chromodynamics (QCD) is different: it is present in the classical theory with massless quarks but is broken upon quantization by the axial anomaly. The anomaly persists at every temperature, yet its observable effects can weaken. Can hot matter nevertheless behave as though this symmetry were restored at long distances? Whether such effective axial $U(1)$ restoration occurs depends on how microscopic quark and gluon dynamics governs the strength and spatial range of axial breaking. This review brings together theoretical developments and first-principles lattice QCD calculations. We examine how gluon-field topology shapes the low-lying Dirac modes and their correlations, how these modes contribute to axial breaking at different spatial scales, and what this implies for the order and critical behavior of the chiral phase transition as quark masses approach zero.
Comments31 pages, Contribution to the Encyclopedia of Nuclear Physics
