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

为了解释量子色动力学（QCD）中的夸克禁闭，我们提出了一种称为拓扑场论微扰变形的规范理论。我们提出了一个修改版本的最大阿贝尔（MA）规范。我们证明了由于Parisi-Sourlas降维，四维时空中修正MA规范的规范固定项约化为二维非线性sigma模型，另一方面，我们将Diakonov和Petrov的一个非阿贝尔Stokes定理推广到SU（2）和SU（N）情形.这个版本是非常有效的理解夸克禁闭的基础上的对偶超导图片QCD.事实上，威尔逊环可以重写的磁超导电流.在上述改造的框架内，我们推导了威尔逊环的期望值的面积律，利用上述非阿贝尔斯托克斯定理.在SU（N）情形下，计算采用了瞬子和大N。这些结果暗示了QCD中的夸克禁闭，为了使QCD在MA规范（非线性规范）中的重整化，四鬼相互作用是必不可少的。我们证明了在自动包含四鬼相互作用的修正MA规范中会发生鬼-反鬼凝聚，并且非对角胶子和非对角鬼获得非零质量。非对角分量的质量不为零证明了Abel规范理论的优势，通过对所有非对角分量的积分，我们可以得到一个Abel规范理论，称为Abel投影有效规范理论（APEGT），它是QCD的低能有效理论。我们从QCD导出了对偶Ginzburg-Landau理论，它表示QCD真空的对偶超导电性。

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.