标题： 基于 instanton 的 QCD 随机矩阵模型中夸克-胶子等离子体的手征对称性的命运 显示英文标题

标题： Fate of Chiral Symmetries in the Quark-Gluon Plasma from an Instanton-Based Random Matrix Model of QCD

摘要： 我们提出了一种理解QCD高温相下手征对称性实现的新方法。基于简单的自由瞬子气体精确描述晶格重叠狄拉克算符谱的最低部分这一发现，我们提出了一个基于瞬子的具有动力学夸克的QCD随机矩阵模型。对该模型的模拟表明，即使对于小的夸克质量，由于自由瞬子的稀疏气体作用，狄拉克谱密度在原点处也存在奇异性。尽管由轻动力学夸克介导的相互作用会产生小的瞬子-反瞬子分子，但这些分子不会影响谱的奇异部分，且该奇异部分被证明在手征极限下主导Banks-Casher型求和。通过推广Banks-Casher公式以处理奇异谱，我们展示了在手征极限下，若有至少两个无质量夸克味道，则手征凝聚量将消失。我们的模型还暗示了一种可能解决长期争论的方法，因为它表明对于两个无质量夸克味道， $U(1)_{A}$ 对称性很可能在任意高的有限温度下仍保持破缺。 显示英文摘要

摘要： We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the lattice overlap Dirac operator, we propose an instanton-based random matrix model of QCD with dynamical quarks. Simulations of this model reveal that even for small quark mass the Dirac spectral density has a singularity at the origin, caused by a dilute gas of free instantons. Even though the interaction, mediated by light dynamical quarks creates small instanton-antiinstanton molecules, those do not influence the singular part of the spectrum, and this singular part is shown to dominate Banks-Casher type sums in the chiral limit. By generalizing the Banks-Casher formula for the singular spectrum, we show that in the chiral limit the chiral condensate vanishes if there are at least two massless flavors. Our model also indicates a possible way of resolving a long-standing debate, as it suggests that for two massless quark flavors the $U(1)_{A}$ symmetry is likely to remain broken up to arbitrarily high finite temperatures.