Dark monopoles and SL(2, ℤ) duality

We explore kinetic mixing between two Abelian gauge theories that have both electric and magnetic charges. When one of the photons becomes massive, novel effects arise in the low-energy effective theory, including the failure of Dirac charge quantization as particles from one sector obtain parametrically small couplings to the photon of the other. We maintain a manifest SL(2, ℤ) duality throughout our analysis, which is the diagonal subgroup of the dualities of the two un-mixed gauge theories.