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In the presence of an anomalous CP phase in a U(1) gauge theory, a monopolebecomes a dyon via the Witten effect. When the anomalous CP phase is promotedto a dynamical field, the axion, the electric charge of the dyon changesaccording to the coherent motion of the axion oscillation. Once the electriccharge exceeds a certain threshold, the Schwinger pair production of chargedparticles becomes efficient near the surface of the dyon. Thesenon-perturbative effects lead to the back reaction of the axion dynamics bycausing the dissipation of the axion oscillation energy and the change of theeffective potential due to the Witten effect. Taking these effects intoaccount, we consider the dynamics of the whole system, including the axion,monopole, and charged heavy vector bosons, and discuss to what extent the axionabundance is modified. We also discuss the electric dipole radiation from abound state of a monopole-anti-monopole pair due to the axion coherentoscillations.

Dissipation of axion energy via the Schwinger and Witten effects