Abstract
In axion-Maxwell theory at the minimal axion-photon coupling, we find non-invertible 0- and 1-form global symmetries arising from the naive shift and center symmetries. Since the Gauss law is anomalous, there is no conserved, gauge-invariant, and quantized electric charge. Rather, using half higher gauging, we find a non-invertible Gauss law associated with a non-invertible 1-form global symmetry, which is related to the Page charge. These symmetries act invertibly on the axion field and Wilson line, but non-invertibly on the monopoles and axion strings, leading to selection rules related to the Witten effect. We also derive various crossing relations between the defects. The non-invertible 0- and 1-form global symmetries mix with other invertible symmetries in a way reminiscent of a higher-group symmetry. Using this non-invertible higher symmetry structure, we derive universal inequalities on the energy scales where different infrared symmetries emerge in any renormalization group flow to the axion-Maxwell theory. Finally, we discuss implications for the Weak Gravity Conjecture and the Completeness Hypothesis in quantum gravity.
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Acknowledgments
We are grateful to I. Bah, T. D. Brennan, C. Cordova, B. Heidenreich, P.-S. Hsin, Z. Komargodski, J. Maldacena, G. W. Moore, K. Ohmori, S. Pufu, M. Reece and S. Seifnashri for useful discussions. We thank T. D. Brennan, J. Kaidi, K. Ohmori, I. Valenzuela, and Y. Zheng for comments on a draft. HTL is supported in part by a Croucher fellowship from the Croucher Foundation, the Packard Foundation and the Center for Theoretical Physics at MIT. The work of SHS was supported in part by NSF grant PHY-2210182. We thank the Simons Collaboration on Global Categorical Symmetries for its hospitality during a conference and a school. SHS thanks Harvard University for its hospitality during the course of this work. The authors of this paper were ordered alphabetically.
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Choi, Y., Lam, H.T. & Shao, SH. Non-invertible Gauss law and axions. J. High Energ. Phys. 2023, 67 (2023). https://doi.org/10.1007/JHEP09(2023)067
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DOI: https://doi.org/10.1007/JHEP09(2023)067