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 {pi}{sup 0}, to the magnetic field via the axial triangle anomaly. We show that, in vacuum, above a value of B{approx}m{sub {pi}}{sup 2}/e, a metastable object appears - the {pi}{sup 0} domain wall. Because of the axial anomaly, the wall carries a baryon number surface density proportional to B. As a result, for B > or approx. 10{sup 19} G a stack of parallel {pi}{sup 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 > or approx. 10{sup 17}-10{sup 18} G transform the color-superconducting ground state of QCD into new phases containing stacks of axial isoscalar ({eta} or {eta}{sup '}) 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{sup 14}-10{sup 15} G.