Axial anomaly and magnetism of nuclear and quark matter

D. T. Son and M. A. Stephanov
Phys. Rev. D 77, 014021 – Published 23 January 2008

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 π0, to the magnetic field via the axial triangle anomaly. We show that, in vacuum, above a value of Bmπ2/e, a metastable object appears—the π0 domain wall. Because of the axial anomaly, the wall carries a baryon number surface density proportional to B. As a result, for B1019G a stack of parallel π0 domain walls is energetically more favorable than nuclear matter at the same density. Similarly, at higher densities, somewhat weaker magnetic fields of order B10171018G transform the color-superconducting ground state of QCD into new phases containing stacks of axial isoscalar (η or η) 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 10141015G.

  • Received 19 October 2007

DOI:https://doi.org/10.1103/PhysRevD.77.014021

©2008 American Physical Society

Authors & Affiliations

D. T. Son

  • Institute for Nuclear Theory, University of Washington, Seattle, Washington 98195-1550, USA

M. A. Stephanov

  • Department of Physics, University of Illinois, Chicago, Illinois 60607, USA

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Vol. 77, Iss. 1 — 1 January 2008

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