Fermionic domain-wall Skyrmions of QCD in a magnetic field

TL;DR

This paper reveals that in strong magnetic fields, the lowest-energy domain-wall Skyrmions in low-energy QCD are fermions with baryon number one, contrasting previous bosonic findings, and explores their phase boundaries.

Contribution

It demonstrates that the minimal domain-wall Skyrmions are fermions with baryon number one, and analyzes their relation to the chiral soliton lattice phase in QCD.

Findings

Minimum domain-wall Skyrmions are fermions with baryon number one.

Bosonic Skyrmions can split into two fermionic Skyrmions without energy cost.

The phase boundary between CSL and Skyrmion phases remains unchanged.

Abstract

The ground state of low-energy QCD matter in strong magnetic fields is either a chiral soliton lattice (CSL), a periodic array of neutral pion domain walls (chiral solitons) perpendicular to the magnetic field, or domain-wall Skyrmion phase, in which Skyrmions are induced on top of the CSL. Previously found domain-wall Skyrmions are bosons with the baryon number two. In this paper, we show that the minimum domain-wall Skyrmions are fermions with baryon number one; a bosonic domain-wall Skyrmion can be separated without energy cost into two fermionic domain-wall Skyrmions attached on the opposite sides of a chiral soliton. The phase boundary between the CSL and domain-wall Skyrmion phases is unchanged. In the chiral limit, the CSL reduces to a linearly dependent neutral pion on the direction of the magnetic field, while fermionic domain-wall Skyrmions sit in an equal distance of half a period.