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Non-invertible Gauss law and axions

  • Regular Article - Theoretical Physics
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  • Published: 12 September 2023
  • Volume 2023, article number 67, (2023)
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Non-invertible Gauss law and axions
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  • Yichul Choi  ORCID: orcid.org/0000-0002-8491-14551,2,
  • Ho Tat Lam3 &
  • Shu-Heng Shao1 

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A preprint version of the article is available at arXiv.

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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  1. C.N. Yang Institute for Theoretical Physics, Stony Brook University, 100 Nicolls Rd, Stony Brook, NY, 11794, USA

    Yichul Choi & Shu-Heng Shao

  2. Simons Center for Geometry and Physics, Stony Brook University, 100 Nicolls Rd, Stony Brook, NY, 11794, USA

    Yichul Choi

  3. Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA, 02139, USA

    Ho Tat Lam

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  1. Yichul Choi
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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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  • Received: 09 January 2023

  • Accepted: 28 August 2023

  • Published: 12 September 2023

  • DOI: https://doi.org/10.1007/JHEP09(2023)067

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Keywords

  • Anomalies in Field and String Theories
  • Global Symmetries
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