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.

为了解释量子染色体动力学（QCD）中的夸克限制，我们提出了对尺度理论的重新制定，称为拓扑场理论的扰动变形。我们提出了最大的Abelian（MA）仪表的修改版本。我们已经表明，在四个时空维度上修改的MA量表的量规固定项减少到非线性Sigma模型，这是两个维度的二维，这是由于Parisi-Sourlas维度减少的。另一方面，我们将Diakonov和Petrov的非 - 阿伯里亚人Stokes定理的版本扩展为SU和SU（SU）的案例（SU（SU）案例（2）案例（2）。该版本非常有效地根据QCD的双重超导体图片来理解夸克限制。该计算由intsanton和SU（N）情况的大N进行。这些结果暗示QCD中的夸克限制。对于QCD在MA仪表（非线性仪表）中的重差异性，四晶体相互作用是必不可少的。我们已经表明，幽灵 - 抗螺旋体的凝结发生在修改后的MA仪表中，该仪表自动包括四个玻璃体相互作用，并且偏高的Gluon和Off-Diagonal Ghost获得了非呈现群体。 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表达QCD真空的双重导导率。