Charge non-conservation, dequantisation, and induced electric dipole   moments in varying-alpha theories
  We note that in extensions of the Standard Model that allow for a varying fine structure constant, alpha, all matter species, apart from right-handed neutrinos, will gain an intrinsic electric dipole moment (EDM). In a large subset of varying-alpha theories, all such particle species will also gain an effective electric charge. This charge will in general not be quantised and can result in macroscopic non-conservation of electric charge. 
Douglas J. Shaw