Physical implications of the electromagnetic duality anomaly

Determine the physical implications of the electromagnetic duality anomaly for quantized source-free Maxwell fields propagating in curved spacetimes with non-vanishing gravitational Chern–Pontryagin density, particularly whether background curvature induces spontaneous electromagnetic circular polarization via asymmetric creation of right- and left-handed photons from the quantum vacuum.

Background

Classically, source-free Maxwell theory enjoys a continuous electric–magnetic (SO(2)) duality symmetry, with an associated Noether current and charge that measure the net helicity (circular polarization) of the electromagnetic field. In flat spacetime, this charge is conserved and equals the Stokes V parameter, i.e., the difference in right- and left-handed photon numbers.

The paper shows that, in the quantum theory on curved spacetimes, this duality symmetry is anomalous: the expectation value of the divergence of the duality current acquires a curvature-dependent term proportional to the gravitational Chern–Pontryagin density, implying that the duality charge is not conserved. The authors note that the physical consequences of this anomaly are not yet settled and suggest, by analogy with the chiral anomaly, that it may lead to spontaneous circular polarization through asymmetric creation of right/left photons from the vacuum.