Response of strongly-interacting matter to magnetic field: some exact results

TL;DR

The paper investigates how strongly interacting matter at finite temperature and baryon density responds to external magnetic fields by examining the axial current induced by a uniform magnetic field, parameterized by the axial magnetic susceptibility $\chi$. Using triangle anomalies and a three-point correlator among the axial, isovector, and baryon currents, it derives exact relations: in the chirally restored phase $\chi = \mu/(4\pi^2)$, and in the chirally broken phase $\chi$ is linked to the in-medium $\pi^0 \to \gamma\gamma$ amplitude via $4\pi^2\frac{\partial\chi}{\partial\mu} + g_{\pi^0\gamma\gamma} = 1$. It verifies these relations in a weakly coupled linear sigma model and extends the analysis to realistic electromagnetic coupling with nonzero isospin chemical potential, obtaining $\chi(T,\mu_I,\mu_B) = \frac{e}{4\pi^2}\left(\mu_B+\frac{\mu_I}{2}\right)\left[1 - \frac{7\zeta(3)}{4\pi^2}\frac{m^2}{T^2} + \cdots\right]$. The results show that anomaly coefficients control the magnetic response even at strong coupling and may have implications for magnetized dense matter in neutron stars, including neutrino self-energies.

Abstract

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 beahvior 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 the neutral pion to decay to two photons. We confirm the latter result by calculation in a linear sigma model, where this amplitude is already known in the literature.