标题： 二维QCD类理论的狄拉克谱 显示英文标题

标题： Dirac Spectra of 2-dimensional QCD-like theories

摘要： 我们分析了二维QCD类理论的Dirac谱，既包括连续极限也包括格点情形，并根据具有相同全局对称性的随机矩阵理论对其进行了分类。 这种分类不同于四维QCD，因为反幺正对称性与$\gamma_5$不交换。因此，在手征基中，每个矩阵元的自由度数不由Dyson指标给出。 我们的预测得到了淬火格点模拟中具有两个或三个颜色的QCD的Dirac谱的证实，夸克分别处于基本表示和伴随表示下。 谱的普适性类别取决于每个方向上格点数目的奇偶性。 我们的结果表明，它与四维QCD中发现的与随机矩阵理论的一致性在定性上相似。 我们讨论了这一结果对Mermin-Wagner-Coleman定理的影响，并将其置于二维无序系统的背景下。 显示英文摘要

摘要： We analyze Dirac spectra of two-dimensional QCD like theories both in the continuum and on the lattice and classify them according to random matrix theories sharing the same global symmetries. The classification is different from QCD in four dimensions because the anti-unitary symmetries do not commute with $\gamma_5$. Therefore in a chiral basis, the number of degrees of freedom per matrix element are not given by the Dyson index. Our predictions are confirmed by Dirac spectra from quenched lattice simulations for QCD with two or three colors with quarks in the fundamental representation as well as in the adjoint representation. The universality class of the spectra depends on the parity of the number of lattice points in each direction. Our results show an agreement with random matrix theory that is qualitatively similar to the agreement found for QCD in four dimensions. We discuss the implications for the Mermin-Wagner-Coleman theorem and put our results in the context of two-dimensional disordered systems.