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

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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.