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arXiv 1409.6539hep-phhep-thnucl-th
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解压缩的矩阵模型及其微扰修正

Matrix Models for Deconfinement and Their Perturbative Corrections

Yun Guo

摘要:

规范理论的$SU(N)$中退细化相变的矩阵模型是近年来发展起来的。这些模型只需要很少的参数,就能再现半夸克-胶子等离子体(QGP)区域热力学量的格点结果。它们也被用来计算t Hooft环的行为和研究例外群$G(2)$。在本文中,我们回顾了这些模型的建设的基本思想,并提出了一种新的形式的矩阵模型中的非理想修正。在半QGP区,我们的新模型与以前的晶格模拟结果一致,而在更高温度区,我们的新模型再现了晶格中重标度迹异常的上升趋势,而这是以前的模型所不能得到的。此外,我们还讨论了对热有效势的微扰修正,它可以用来系统地改进高温下的矩阵模型。特别是,我们提供了,第一次,一个分析证明之间的关系的一个和两个回路的有效潜力:两个回路的校正是成比例的一个回路的结果,独立的Polyakov回路的本征值。这是一个非常一般的结果,我们对所有的经典群,包括$SU(N)$,$SO(2N+1)$,$SO(2N)$和$Sp(2N)$都证明了这个结果.

英文摘要:

Matrix models for the deconfining phase transition in $SU(N)$ gauge theories have been developed in recent years. With a few parameters, these models are able to reproduce the lattice results of the thermodynamic quantities in the semi-quark gluon plasma(QGP) region. They are also used to compute the behavior of the 't Hooft loop and study the exceptional group $G(2)$. In this paper, we review the basic ideas of the construction of these models and propose a new form of the non-ideal corrections in the matrix model. In the semi-QGP region, our new model is in good agreement with the lattice simulations as the previous ones, while in higher temperature region, it reproduces the upward trend of the rescaled trace anomaly as found in lattice which, however, can not be obtained from the previous models. In addition, we discuss the perturbative corrections to the thermal effective potential which could be used to systematically improve the matrix models at high temperatures. In particular, we provide, for the first time, an analytical proof of the relation between the one- and two-loop effective potential: two-loop correction is proportional to the one-loop result, independent of the eigenvalues of the Polyakov loop. This is a very general result, we prove it for all classic groups, including $SU(N)$, $SO(2N+1)$, $SO(2N)$ and $Sp(2N)$.

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