Theoretical research of quark-gluon confinement and chiral symmetry breaking by Abelian projection

阿贝尔投影夸克胶子禁闭与手征对称性破缺的理论研究

基本信息

批准号：
10640249
负责人：
KONDO Kei-ichi
金额：
$ 2.3万
依托单位：
Chiba University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640249/
关键词：
quark confinement magnetic monopole topological field theory Stokes theorem Abelian dominance Wilson loop Quantum Chromodynamics monopole dominance 非可換ストークス定理クォークの閉じ込め磁気単極子

项目摘要

In order to explain quark confinement in Quantum Chromodynamics (QCD), we have proposed a reformulation of the gauge theory called the perturbative deformation of a topological field theory. We have proposed a modified version of the Maximally Abelian (MA) gauge. We have shown that the gauge fixing term of the modified MA gauge in four space-time dimensions reduces to the nonlinear sigma model in two dimensions owing to the Parisi-Sourlas dimensional reduction.On the other hand, we have extended a version of non-Abelian Stokes theorem by Diakonov and Petrov which was known for the SU(2) case into the SU(3) and SU(N) case. This version is very efficient to understand quark confinement based on the dual superconductor picture of QCD.In fact, the Wilson loop can be rewritten in terms of the magnetic monopole current.Within the framework of the above reformulation, we have derived the area law of the Wilson loop expectation value by making use of the above non-Abelian Stokes theorem. The calculation was performed by the instanton and the large N for the SU(N) case. These results imply quark confinement in QCD.For the renormalizability of QCD in the MA gauge (nonlinear gauge), a four-ghost interaction is indispensable. We have shown that the ghost-anti-ghost condensation occurs in the modified MA gauge which automatically includes the four-ghost interaction and that the off-diagonal gluon and off-diagonal ghost acquire the non-vanishing masses. Non-vanishing mass for the off-diagonal components gives an evidence for Abelian dominance confirmed by numerical calculations.By integrating out all the off-diagonal components, we can obtain an Abelian gauge theory called the Abelian projected effective gauge theory (APEGT) as a low-energy effective theory of QCD.By making use of the APEGT, we have derived the dual Ginzburg-Landau theory from QCD that expresses the dual superconductivity of QCD vacuum.

为了解释量子色动力学（QCD）中的夸克禁闭，我们提出了一种规范理论的重新表述，称为拓扑场论的微扰变形。我们提出了最大阿贝尔（MA）规范的修改版本。我们已经证明，由于 Parisi-Sourlas 降维，改进的 MA 规范在四个时空维度上的规范固定项简化为二维的非线性 sigma 模型。另一方面，我们扩展了非Diakonov 和 Petrov 提出的阿贝尔斯托克斯定理因将 SU(2) 情况转变为 SU(3) 和 SU(N) 情况而闻名。这个版本对于理解基于 QCD 对偶超导图的夸克禁闭非常有效。事实上，威尔逊环可以用磁单极子电流重写。在上述重构的框架内，我们推导了面积定律利用上述非阿贝尔斯托克斯定理得到威尔逊环期望值。 SU(N) 情况下通过瞬子和大 N 进行计算。这些结果意味着QCD中的夸克禁闭。对于MA规范（非线性规范）中QCD的可重整性，四鬼相互作用是必不可少的。我们已经证明，在修改后的 MA 规范中会发生鬼-反鬼凝聚，该规范自动包含四鬼相互作用，并且非对角胶子和非对角鬼获得非消失质量。非对角线分量的不消失质量为数值计算证实了阿贝尔优势提供了证据。通过积分所有非对角线分量，我们可以获得阿贝尔规范理论，称为阿贝尔投影有效规范理论（APEGT） QCD的低能有效理论。利用APGT，我们从QCD中推导出了表达QCD真空对偶超导性的对偶Ginzburg-Landau理论。