Chiral-imbalance density wave in baryonic matters

Abstract

We propose a new chirality-imbalance phenomenon arising in baryonic/high density matters under a magnetic field. A locally chiral-imbalanced (parity-odd) domain can be created due to the electromagnetically induced U(1)A anomaly in high-density matters. The proposed local-chiral imbalance generically possesses a close relationship to a spatial distribution of an inhomogeneous chiral (pion)-vector current coupled to the magnetic field, in which the inhomogeneity is irrespective to the pion-domain wall configuration formed by neutral pion. To demonstrate such a nontrivial correlation, we take the skyrmion crystal approach to model baryonic/high density matters. Remarkably enough, we find the chirality-imbalance distribution can have a periodicity in a high density region, and that it looks specially propagating (dubbed ‘chiral-imbalance density wave’), when the inhomogeneous chiral condensate develops to take a similar periodic distribution, so-called a chiral density wave. This implies the emergence of a nontrivial density wave for the explicitly broken U(1)A current simultaneously with the chiral density wave for the spontaneously broken chiral-flavor current. We further find that the topological phase transition in the skyrmion crystal model (between skyrmion and half-skyrmion phases) undergoes the deformation of the chiral-imbalance density wave in shape and periodicity. The emergence of this chiral-imbalance density wave could give a crucial contribution to studies on the chiral phase transition, as well as the nuclear matter structure, in compact stars under a magnetic field.