Domain-wall Skyrmion phase of QCD in magnetic field: Gauge field dynamics

TL;DR

This paper investigates the phase transition between chiral soliton lattice and domain-wall Skyrmion phases in QCD under strong magnetic fields, incorporating gauge field dynamics and revealing charged Skyrmions due to chiral anomaly.

Contribution

It extends previous BPS approximation studies by including gauge field dynamics, confirming the phase boundary remains unchanged, and demonstrates Skyrmions are electrically charged.

Findings

Phase boundary between CSL and DWSk phases matches BPS approximation results.

Domain-wall Skyrmions carry electric charge due to chiral anomaly.

Gauge field dynamics do not alter the phase boundary.

Abstract

The ground state of QCD in sufficiently strong magnetic field at finite baryon density is an inhomogeneous state consisting of an array of solitons, called the chiral soliton lattice (CSL). It is, however, replaced in a region with higher density and/or magnetic field by the so-called domain-wall Skyrmion(DWSk) phase where Skyrmions are created on top of the CSL. This was previously proposed within the Bogomol'nyi-Prasad-Sommerfield (BPS) approximation neglecting a gauge field dynamics and taking into account its effect by a flux quantization condition. In this paper, by taking into account dynamics of the gauge field, we show that the phase boundary between the CSL and DWSk phases beyond the BPS approximation is identical to the one obtained in the BPS approximation. We also find that domain-wall Skyrmions are electrically charged with the charge one as a result of the chiral anomaly.