Electromagnetic Duality Anomaly in Curved Spacetimes *

 

Maxwell's equations in the absence of sources are invariant under electric-magnetic duality transformations. This symmetry leads to a constant of motion, via Noether’s theorem, that is given by the net circular polarization of the electromagnetic field. I will describe how this symmetry remains exact also in the quantum theory in Minkowski spacetime, but not necessarily if a gravitational field is present. This implies that the polarization of photons propagating in a gravitational background can change in time, or in other words, that gravity can act as an optically active medium. This is a quantum effect, and it can be understood as the generalization of the well-known chiral anomaly of fermions to fields of spin 1.