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(0), to the magnetic field via the axial triangle anomaly. We show that, in vacuum, above a value of B similar to 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 greater than or similar to 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 greater than or similar to 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.