Strong magnetic fields in compact stars as a macroscopic parity violation phenomenon

We review the results in our recent works on the generation of strong magnetic fields in compact stars driven by the parity violating electroweak interactions between background fermions. The cases of a neutron star, a hybrid star, and a quark star are considered. We formulate the system of kinetic equations for the description of the spectra of the magnetic energy and the magnetic helicity, as well as for the chiral imbalances. Turbulence effects, which can be important for the evolution of small-scale magnetic field, are also taken into account. We find the numerical solution of these equations in case of large- and small-scale magnetic fields in quark matter. The applications of the obtained results for the generation of large-scale magnetic fields in magnetars and for the explanation of magnetar bursts are discussed.