Abstract
In the presence of massive fermions, and assuming a non-vanishing θ-parameter as the only source of CP violation, the Witten effect (a shift in the electric charge of a magnetic monopole due to CP non-conservation) is shown to follow from an anomalous chiral commutator. Next, given the gravitational contribution to the chiral anomaly, the corresponding anomalous commutator for Dirac fermion currents in a gravitational background is derived. From that, we infer the equivalence of θ R ̃ R term in the lagrangian to a shift in the mass parameter of the NUT metric, in proportion to θ. This is interpreted as the gravitational analogue of the Witten effect. Its relevance to certain Kaluza-Klein monopoles is briefly discussed.
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