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Discrete gauging and noninvertible selection rules

Jun Dong1,*, Tim Jeric1,†, Tatsuo Kobayashi1,‡, Ryusei Nishida1,§, and Hajime Otsuka2,3,∥

  • 1Department of Physics, Hokkaido University, Sapporo 060-0810, Japan
  • 2Department of Physics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
  • 3Quantum and Spacetime Research Institute (QuaSR), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

  • *Contact author: j-dong@particle.sci.hokudai.ac.jp
  • †Contact author: t-jeric@particle.sci.hokudai.ac.jp
  • ‡Contact author: kobayashi@particle.sci.hokudai.ac.jp
  • §Contact author: r-nishida@particle.sci.hokudai.ac.jp
  • ∥Contact author: otsuka.hajime@phys.kyushu-u.ac.jp
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Phys. Rev. D 113, 056028 – Published 30 March, 2026

DOI: https://doi.org/10.1103/nsvv-l2dy

Abstract

We clarify selection rules of conjugacy classes of several finite discrete groups where we deal with both gauged and ungauged cases. We find that the selection rules enjoy finite Abelian or non-Abelian discrete symmetries originating from the inner and/or outer automorphism of underlying discrete groups. Since the selection rules of conjugacy classes do not obey conventional grouplike selection rules, they open up new coupling selection rules of fields which are labeled by the conjugacy classes.

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Phys. Rev. D 113, 056028– Published 30 March, 2026
  • Received 11 September 2025
  • Accepted 9 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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