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Axion Mass from Magnetic Monopole Loops
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We show that axions interacting with abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their energy spectrum. The axion potential can also be understood as a type of instanton effect due to a Euclidean monopole worldline winding around its dyon collective coordinate. We calculate this effect, which has features in common with both nonabelian instantons and Euclidean brane instantons. To provide consistency checks, we argue that this axion potential vanishes in the presence of a massless charged fermion and that it is robust against the presence of higher-derivative corrections in the effective Lagrangian. Finally, as a first step toward connecting with particle phenomenology and cosmology, we discuss the regime in which this potential is important in determining the dark matter relic abundance in a hidden sector containing an abelian gauge group, monopoles, and axions.
Forward citations
Cited by 4 Pith papers
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Dark Matter and Baryon Asymmetry from Monopole-Axion Interactions
A rotating QCD axion dissipates kinetic energy via dark monopole dyon transitions, explaining dark matter and baryon asymmetry with a predicted axion decay constant below 10^9 GeV.
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Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
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Self-Consistent Parker Bound on Magnetic Monopoles
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Gravitational waves and dark matter with Witten effect
A dark SU(2) phase transition can produce monopole dark matter, make the axion heavy via the Witten effect, and generate nanohertz gravitational waves matching PTA hints.
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