Dyon in the SU(2)SU(2) Yang--Mills theory with a gauge-invariant gluon mass toward quark confinement

In the previous paper, we have shown the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory with a gauge-invariant mass term for the gluon field being introduced. In this paper, we extend our previous construction of magnetic monopoles to obtain dyons with both magnetic and electric charges. In fact, we solve under the static and spherically symmetric ansatz the field equations of the $SU(2)$ "complementary" gauge-scalar model, which is the $SU(2)$ Yang--Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the novel dyon solution can be identified with the gauge field configuration of a dyon with a minimum magnetic charge in the massive Yang--Mills theory. Moreover, we compare the dyon of the massive Yang--Mills theory obtained in this way with the Julia--Zee dyon in the Georgi--Glashow gauge-Higgs scalar model and the dyonic extension of the Wu--Yang magnetic monopole in the pure Yang--Mills theory. Finally, we identify the novel dyon solution found in this paper with a dyon configuration on $S^1 \times \mathbb{R}^3$ space with nontrivial holonomy and propose to use it to understand the confinement/deconfinement phase transition in the Yang--Mills theory at finite temperature, instead of using the dyons constituting the Kraan--van Baal--Lee--Lu caloron.Comment: 24 pages, 11 figure

Type of dual superconductivity for the SU(2)SU(2) Yang--Mills theory

We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the $U(1)$ gauge-scalar model to obtain the static vortex solution in the whole range without restricting to the long-distance region. Then we use the resulting magnetic field of the vortex to fit the gauge-invariant chromoelectric field connecting a pair of quark and antiquark which was measured by numerical simulations for $SU(2)$ Yang--Mills theory on a lattice. This result improves the accuracy of the fitted value for the Ginzburg--Landau parameter to reconfirm the type I dual superconductivity for quark confinement which was claimed by preceding works based on a fitting using the Clem ansatz. Moreover, we calculate the Maxwell stress tensor to obtain the distribution of the force around the flux tube. This result suggests that the attractive force acts among chromoelectric flux tubes, in agreement with the type I dual superconductivity.Comment: 15 pages, v4-published versio