Abstract
We consider the general form of the axion coupling to photons in the axion-Maxwell theory. On general grounds this coupling takes the form of a monodromic function of the axion, which we call g(a), multiplying the Chern-Pontryagin density \( F\overset{\sim }{F} \) of the photon. We show that the non-linearity of g(a) is a spurion for the shift symmetry of the axion. In this context, when g(a) ≠ ℤa, the linearized coupling of the axion g′(a) is not quantized and there is a correlated mass term for the axion. Singularities in g(a) due to the fast rearrangement of degrees of freedom are shown to have corresponding cusps and singularities in the axion potential. We derive the general form of g(a) for the QCD axion, axions with perturbatively broken shift symmetries and axions descending from extra dimensions. In all cases, we show that there is a uniform general form of the monodromic function g(a) and it is connected to the axion potential.
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Acknowledgments
We would like to thank Mario Reig for useful comments on the draft and John March-Russell, Michael Nee and Thomas Harvey for helpful discussions. PA is supported by the STFC under Grant No. ST/T000864/1. AP is supported by a STFC Studenship No. 2397217 and Prins Bernhard Cultuurfondsbeurs No. 40038041 made possible by the Pieter Beijer fonds and the Data-Piet fonds.
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Agrawal, P., Platschorre, A. The monodromic axion-photon coupling. J. High Energ. Phys. 2024, 169 (2024). https://doi.org/10.1007/JHEP01(2024)169
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DOI: https://doi.org/10.1007/JHEP01(2024)169