Axial anomaly and magnetism of nuclear and quark matter
D. T. Son and M. A. Stephanov

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 $B\sim m_\pi^2/e$, a metastable object appears---the $\pi^0$ domain wall. Due to the axial anomaly, the wall carries a baryon number surface density proportional to $B$. As a result, for $B\gtrsim 10^{19} ~\textrm G$ 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 $B\gtrsim 10^{17}-10^{18} ~\textrm G$ 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 $10^{14}-10^{15} ~\textrm G$.

© 2008 The American Physical Society.