  Condensation of the Abelian monopoles and the center vortices leads to
confinement of color in low temperature phase of Yang-Mills theory. We stress
that these topological magnetic degrees of freedom are also very important in
the deconfinement regime: at the point of the deconfinement phase transition
both the monopoles and the vortices are released into the thermal vacuum
contributing, in particular, to the equation of state and, definitely, to
transport properties of the hot gluonic medium. Thus, we argue that a novel,
magnetic component plays a crucial role. On the other hand, it was demonstrated
that an effective three-dimensional description can be brought, beginning with
high temperatures, down to the critical temperature by postulating existence of
a system of 3d Higgs fields. We propose to identify the 3d color-singlet Higgs
field with the 3d projection of the 4d magnetic vortices. Such identification
fits well the 3d properties of the theory and contributes to interpretation of
the magnetic component of the Yang-Mills plasma.

High Energy Physics - Phenomenology;High Energy Physics - Lattice;High Energy Physics - Theory