Axial anomaly and magnetism of nuclear and quark matter

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 ^0, to the magnetic field via the axial triangle anomaly. We show that, in vacuum, above a value of Bm_^2/e, a metastable object appears---the ^0 domain wall. Because of the axial anomaly, the wall carries a baryon number surface density proportional to B. As a result, for B10^19 G a stack of parallel ^0 domain walls is energetically more favorable than nuclear matter at the same density. Similarly, at higher densities, somewhat weaker magnetic fields of order B10^17--10^18 G transform the color-superconducting ground state of QCD into new phases containing stacks of axial isoscalar (or ^') 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.