Dynamics with Vector Condensates at Finite Density in QCD and Beyond

I describe the dynamics in recently revealed phases with vector condensates of gauge fields in dense QCD (gluonic phase) and other gauge models. In this case, the Higgs mechanism is provided by condensates of gauge (or gauge plus scalar) fields. Because most of the initial symmetries in such systems are spontaneously broken, their dynamics is very rich. In particular, by using the Ginzburg-Landau approach, the existence of a gluonic phase with both the rotational symmetry and the electromagnetic U(1) being spontaneously broken was established. In other words, this phase describes an anisotropic superconductor. In the dual (confinement) description of this dynamics in dense two-flavor QCD, there are light exotic vector hadrons in the spectrum, some of which condense. There are also vortex-like and roton-like excitations in these phases.