Narrow Results

The dual superconductor picture of the QCD vacuum is thought to describe the various aspects of the strong interaction including confinement. Ordinary superconductivity is described by the Ginzburg–Landau (GL) equation. In the present work we show that it is possible to arrive at a GL-like equation from pure SU(2) gauge theory. This is accomplished by using Abelian projection to split the SU(2) gauge fields into an Abelian subgroup and its coset. The two gauge field components of the coset part act as the effective, complex, scalar field of the GL equation. The Abelian part of the SU(2) gauge field is then analogous to the electromagnetic potential in the GL equation. An important feature of the dual superconducting model is for the GL Lagrangian to have a spontaneous symmetry breaking potential, and the existence of Nielsen–Olesen flux tube solutions. Both of these require a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

The well-known topological monopoles originally investigated by 't Hooft and Polyakov are known to arise in classical Yang–Mills–Higgs theory. With a pure gauge theory, it is known that the classical Yang–Mills field equation do not have such finite energy configurations. Here we argue that such configurations may arise in a semi-quantized Yang–Mills theory, where the original gauge group, SU(3), is reduced to a smaller gauge group, SU(2), and with some combination of the coset fields of the SU(3) to SU(2) reduction acting as effective scalar fields. The procedure is called semi-quantized since some of the original gauge fields are treated as quantum degrees of freedom, while others are postulated to be effectively described as classical degrees of freedom. Some speculation is offer on a possible connection between these monopole configurations and the confinement problem, and the nucleon spin puzzle.

In the present work we show that it is possible to arrive at a Ginzburg-Landau (GL) like equation from pure SU(2) gauge theory. This has a connection to the dual superconducting model for color confinement where color flux tubes permanently bind quarks into color neutral states. The GL Lagrangian with a spontaneous symmetry breaking potential, has such (Nielsen-Olesen) flux tube solutions. The spontaneous symmetry breaking requires a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.

First, we give a gauge-independent definition of chromomagnetic monopoles in $SU(N)$ Yang–Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give a nontrivial contribution to the Wilson loop operator for understanding the area law of the Wilson loop average. Next, we discuss how the magnetic monopole condensation picture are compatible with the vortex condensation picture as another promising scenario for quark confinement. We analyze the profile function of the magnetic flux tube as the non-Abelian vortex solution of $U(N)$ gauge-Higgs model, which is to be compared with numerical simulations of the $SU(N)$ Yang–Mills theory on a lattice. This analysis gives an estimate of the string tension based on the vortex condensation picture, and possible interactions between two non-Abelian vortices.

In the preceeding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we discuss the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. We investigate chromomagnetic monopole currents induced by chromoelectric flux in both confinement and deconfinement phase by the numerical simulations on a lattice at finite temperature, and discuss the role of the chromomagnetic monopole in the confinement/deconfinement phase transition.

The study of supersymmetric quantum theory of superconductivity has been undertaken in a broader sense. The main features of supersymmetric quantum mechanics have been derived in a straightforward manner and the consequences of supersymmetric breaking have been analyzed in terms of the possibility of occurrence of superconductivity, dual superconductivity and color superconductivity.

First, we give a gauge-independent definition of chromomagnetic monopoles in SU(N) Yang-Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give a nontrivial contribution to the Wilson loop operator for understanding the area law of the Wilson loop average. Next, we discuss how the magnetic monopole condensation picture are compatible with the vortex condensation picture as another promising scenario for quark confinement. We analyze the profile function of the magnetic flux tube as the non-Abelian vortex solution of U(N) gauge-Higgs model, which is to be compared with numerical simulations of the SU(N) Yang-Mills theory on a lattice. This analysis gives an estimate of the string tension based on the vortex condensation picture, and possible interactions between two non-Abelian vortices.

In the preceeding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we discuss the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. We investigate chromomagnetic monopole currents induced by chromoelectric flux in both confinement and deconfinement phase by the numerical simulations on a lattice at finite temperature, and discuss the role of the chromomagnetic monopole in the confinement/deconfinement phase transition.

The dual superconductivity is the promising mechanism for quark confinement. We have proposed the non-Abelian dual superconductivity picture in the SU(3) Yang-Mills theory, and already presented numerical evidences for the restricted field dominance and the non-Abelian magnetic monopole dominance in the string tension, by applying our new formulation of Yang-Mills theory to a lattice. In this talk, we focus on the non-Abelian dual Meissner effect and the type of dual superconductivity. We find that the measured chromo-electric flux tube between a quark and antiquark pair strongly supports the non-Abelian dual Meissner effect due to non-Abelian magnetic monopoles. Moreover, we give a remarkable result that the type of the resulting dual superconductor is the type I in SU(3) Yang-Mills, rather than the border between the type I and II, in marked contrast to the SU(2) case.

We give numerical evidences for the non-Abelian dual superconductivity due to non-Abelian magnetic monopoles in SU(3) Yang-Mills theory as a mechanism for quark confinement, based on our new formulation of lattice gauge theory.