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Noninvertible chiral symmetry and axions under electromagnetic duality

Gongjun Choi1,*, Tony Gherghetta2,†, and John Terning3,‡

  • 1William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 3Center for Quantum Mathematics and Physics (QMAP), Department of Physics, University of California, Davis, California 95616, USA

  • *Contact author: choi0988@umn.edu
  • †Contact author: tgher@umn.edu
  • ‡Contact author: jterning@gmail.com
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Phys. Rev. D 112, 095023 – Published 17 November, 2025

DOI: https://doi.org/10.1103/vdcp-k462

Abstract

We study the implications of noninvertible chiral symmetry in a four-dimensional U(1) gauge theory coupled to massless fermions with electromagnetic SL(2,Z) duality. This is done by deriving the Adler-Bell-Jackiw anomaly of massless QED in the dual frame that is used to explicitly construct the symmetry defect operator as well as the conserved two-form symmetry current. As expected, the noninvertible chiral symmetry is covariant under the duality transformation. This has implications for understanding the nature of kinetic and topological terms in the dual frame and for axion electrodynamics. In particular, we show that to generate an axion potential from a dyon loop, the one-form magnetic symmetry must be explicitly broken by a mutually nonlocal charged state with nonzero pairwise helicity.

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Phys. Rev. D 112, 095023– Published 17 November, 2025
  • Received 26 September 2025
  • Accepted 31 October 2025
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