Electric-magnetic duality in the quantum theory

It is known that an electric-magnetic duality transformation is a symmetry of the classical source-free Maxwell theory in generic spacetimes. This provides a conserved Noether charge, physically related to the polarization state of the electromagnetic field. We shall argue that this conservation law fails to hold at the quantum level in presence of a background classical gravitational field with non-trivial dynamics, as determined by the Chern-Pontryagin invariant. This is the spin-1 analog of the chiral anomaly for massless Dirac fermions.