Large-Nc gauge theory and chiral random matrix theory
Large-Nc gauge theory and chiral random matrix theory
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大数控规范理论和手性随机矩阵理论
DOI：
10.1103/physrevd.88.025046
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
J.-W. Lee and N. Yamada
中科院分区：
文献类型：
--
作者：
M. Hanada;J.-W. Lee and N. Yamada
讨论了如何将展开式和手征无规矩阵理论应用于大规范理论的研究。我们首先澄清的参数区域中，这两种方法都是有效的。虽然费米子的质量固定在标准的大参数（'t Hooft大极限），必须适当地缩放一定的负幂，以便规范理论被描述的。然后，虽然这两个限制是不兼容的一般情况下，我们表明，手征对称性的故障可以检测到结合大参数和一些照顾。作为一个具体的例子，我们数值研究了在格点上引入重伴随费米子作为中心对称性以保持红外物理的完整性的四维规范理论。通过研究伴随表象中无质量探测费米子的狄拉克算符的低本征值，我们发现手征对称确实以预期的破缺模式破缺。这一结果再现了一个众所周知的事实，手征对称性自发破缺的puregauge理论在大和大体积的限制，因此支持的有效性的组合方法。我们还提供了一个解释的差距和unexpectedscaling，这两者都是观察到的狄拉克光谱。
We discuss how theexpansion and the chiral random matrix theory () can be used in the study of large-gauge theories. We first clarify the parameter region in which each of these two approaches is valid. While the fermion massis fixed in the standard large-arguments (’t Hooft large-limit),must be scaled appropriately with a certain negative power ofin order for the gauge theories to be described by the. Then, although these two limits are not compatible in general, we show that the breakdown of chiral symmetry can be detected by combining the large-argument and thewith some care. As a concrete example, we numerically study the four-dimensionalgauge theory withheavy adjoint fermions, introduced as the center symmetry preserver keeping the infrared physics intact, on alattice. By looking at the low-lying eigenvalues of the overlap-Dirac operator for a massless probe fermion in the adjoint representation, we find that the chiral symmetry is indeed broken with the expected breaking pattern. This result reproduces a well-known fact that the chiral symmetry is spontaneously broken in the puregauge theory in the large-and the large-volume limit and therefore supports the validity of the combined approach. We also provide an interpretation of the gap and unexpectedscaling, both of which are observed in the Dirac spectrum.