Response of strongly interacting matter to a magnetic field: Some exact results

We derive some exact results concerning the response of strongly interacting matter to external magnetic fields. Our results come from consideration of triangle anomalies in medium. First, we define an “axial magnetic susceptibility,” then we examine its behavior in two-flavor QCD via response theory. In the chirally restored phase, this quantity is proportional to the fermion chemical potential, while in the phase of broken chiral symmetry it can be related, through triangle anomalies, to an in-medium amplitude for ${\pi }^0\to 2\gamma$. We confirm the latter result by calculation in a linear sigma model, where this amplitude is already known in the literature.