# Chiral-Imbalance Density Wave in Baryonic Matters

## TL;DR

This paper introduces a novel chiral-imbalance density wave phenomenon in high-density baryonic matter under magnetic fields, modeled via skyrmion crystals, revealing implications for chiral phase transitions and nuclear matter in compact stars.

## Contribution

It proposes the existence of a chiral-imbalance density wave linked to inhomogeneous chiral condensates, demonstrated through skyrmion crystal modeling, and explores its deformation during topological phase transitions.

## Key findings

- Chiral-imbalance density wave forms in high-density matter with magnetic fields.
- The wave shape and periodicity change during skyrmion to half-skyrmion phase transition.
- Potential impact on understanding chiral phase transition and nuclear matter in stars.

## Abstract

We propose a new chirality-imbalance phenomenon arising in baryonic/high dense 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-dense matters. The proposed local-chiral imbalance generically possesses a close relationship to a spacial distribution of an inhomogeneous chiral (pion)-vector current coupled to the magnetic field. To demonstrate such a nontrivial correlation, we take the skyrmion crystal approach to model baryonic/high dense matters. Remarkably enough, we find the chirality-imbalance distribution takes a wave form in a high density region (dobbed ``chiral-imbalance density wave''), when the inhomogeneous chiral condensate develops to form 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.