Axial anomaly and magnetism of nuclear and quark matter

TL;DR

This paper explores how strong magnetic fields influence the QCD ground state at finite density, revealing the formation of domain walls and ferromagnetic states driven by the axial anomaly, with implications for neutron star magnetism.

Contribution

It demonstrates the role of the axial anomaly in creating novel magnetic and topological phases in dense QCD matter, including pi^0 domain walls and ferromagnetic Goldstone current states.

Findings

Pi^0 domain walls become energetically favorable above B ~ m_pi^2/e.

Stacked pi^0 domain walls can dominate nuclear matter at B ~ 10^{19} G.

Goldstone current states exhibit ferromagnetism with magnetic fields of 10^{14}-10^{15} G in neutron stars.

Abstract

We consider the response of the QCD ground state at finite baryon density to a strong magnetic field B. We point out the dominant role played by the coupling of neutral Goldstone bosons, such as pi^0, to the magnetic field via the axial triangle anomaly. We show that, in vacuum, above a value of B ~ m_pi^2/e, a metastable object appears - the pi^0 domain wall. Because of the axial anomaly, the wall carries a baryon number surface density proportional to B. As a result, for B ~ 10^{19} G a stack of parallel pi^0 domain walls is energetically more favorable than nuclear matter at the same density. Similarly, at higher densities, somewhat weaker magnetic fields of order B ~ 10^{17}-10^{18} G transform the color-superconducting ground state of QCD into new phases containing stacks of axial isoscalar (eta or eta') domain walls. We also show that a quark-matter state known as ``Goldstone current state,'' in which a gradient of a Goldstone field is spontaneously generated, is ferromagnetic due to the axial anomaly. We estimate the size of the fields created by such a state in a typical neutron star to be of order 10^{14}-10^{15} G.