  Many recent experiments addressed manifestations of electronic crystals,
particularly the charge density waves, in nano-junctions, under electric field
effect, at high magnetic fields, together with real space visualizations by STM
and micro X-ray diffraction. This activity returns the interest to stationary
or transient states with static and dynamic topologically nontrivial
configurations: electronic vortices as dislocations, instantons as phase slip
centers, and ensembles of microscopic solitons. Describing and modeling these
states and processes calls for an efficient phenomenological theory which
should take into account the degenerate order parameter, various kinds of
normal carriers and the electric field. Here we notice that the commonly
employed time-depend Ginzburg-Landau approach suffers with violation of the
charge conservation law resulting in unphysical generation of particles which
is particularly strong for nucleating or moving electronic vortices. We present
a consistent theory which exploits the chiral transformations taking into
account the principle contribution of the fermionic chiral anomaly to the
effective action. The resulting equations clarify partitions of charges,
currents and rigidity among subsystems of the condensate and normal carriers.
On this basis we perform the numerical modeling of a spontaneously generated
coherent sequence of phase slips - the space-time vortices - serving for the
conversion among the injected normal current and the collective one.
