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Studies of Lattice Garuge Models with θ-Term by Numerical Simulations and Renormalization Group Method

含θ项格鲁格模型的数值模拟和重正化群法研究

基本信息

批准号：
11640248
负责人：
IMACHI Gasahiro
金额：
$ 1.66万
依托单位：
YANAGATA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640248/
关键词：
Lattice gauge theory CP^<N-1> model θ-term topological charge distribution strong CP violation first order phase transition confinement fixed point action CP^^{N-1}模型テータ項 CP^{N-1}模型ハルデーン予想

项目摘要

Much progress was done in understanding of non-perturbative aspect of gauge theories by lattice gauge theory approach. Studies up to now were mainly about the systems without θ-term, i.e., topological term. The role of θ-term is not known well. Two dimensional CP^<N-1> model and four dimensional QCD have many common properties. Schierholz suggested the value of θ will go to zero in continuum limit. If it is true the problem of Strong CP violation is reduced to the dynamical property of the gauge system itself. When the system has θ-term, numerical simulation will be difficult because the Boltzmann factor becomes complex number and cannot be used as the probability weight. The aim of this project is to develop the method to perform numerical simulations about the system with θ-term. Topological charge distribution P(Q) is obtained with real positive Boltzmann weight without θ-term. Then the partition function is obtained by the Fourier series with weight exp(iθQ/2π). We found free energy shows "flattening" at some value of θ. The origin of this flattening, in our investigation, is due to the statistical error in P(Q = 0) but not due to the first order phase transition (this latter interpretation is made by Schieholz). We also studied the system based on "fixed point action", which is expected to be closer to continuum limit. Scaling behavior is found in CP^3 but not in CP^1 model. We are now studying Z_N lattice gauge theory by real space renormalization group approach to investigate "oblique confinement" which is expected by Cardy- Rabinovici using free energy argument.

格点规范理论在理解规范理论的非微扰方面取得了很大进展。迄今为止的研究主要是针对无θ项的系统，即，拓扑术语θ项的作用还不清楚。二维CP_n<N-1>模型和四维QCD有许多共同的性质。希尔霍尔茨认为θ在连续极限下趋于零。如果这是真的，那么强CP破坏问题就归结为规范系统本身的动力学性质。当系统具有θ项时，由于玻尔兹曼因子为复数，不能作为概率权重，数值模拟将变得困难。本计画的目的是发展对含θ项系统进行数值模拟的方法。用无θ项的真实的正Boltzmann权得到拓扑电荷分布P（Q）.然后通过权函数exp（iθQ/2π）的Fourier级数得到配分函数。我们发现自由能在θ的某个值处表现出“平坦化”。在我们的研究中，这种平坦化的起源是由于P（Q = 0）中的统计误差，而不是由于一阶相变（后者的解释是由Schieholz作出的）。我们还研究了基于“不动点作用”的系统，期望它更接近连续极限。在CP^3模型中发现了标度行为，而在CP^1模型中没有。我们现在用真实的空间重整化群方法研究Z_N格点规范理论，以探讨Cardy-Rabinovici用自由能论证所期望的“斜禁闭”。