Non-invertible Selection Rules from Generalized Discrete Gauging of Finite Non-Abelian Symmetries
Abstract
We investigate non-invertible selection rules originating from the discrete H-gauging of theories with an underlying discrete global symmetry group G. To systematically describe these theories, we formulate a general framework for H-gauged models that incorporates generalized field transformations. Our approach naturally accommodates non-Abelian groups, for which multidimensional irreducible representations play an essential role. In such models with non-Abelian groups, the transformations induced by H non-trivially mix the internal components of G-multiplets, potentially projecting out specific degrees of freedom. Consequently, conventional selection rules based on standard tensor product decompositions or conjugacy classes become insufficient. By analyzing the full semidirect product G rtimes H, we introduce projected characters to derive necessary and sufficient conditions for non-vanishing n-point bare couplings. Furthermore, we demonstrate that the remaining field components obey an associative fusion-like algebra governed by their Clebsch-Gordan coefficients. Phenomenologically, these selection rules restrict allowed interactions and impose specific relations among coupling constants. We illustrate our results through concrete examples, including Δ(54) ≅ Δ(27)rtimes ℤ2 and S4 ≅ A4 rtimes ℤ2.
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BibTeX
@misc{ohki2026noninvertible,
title = {{Non-invertible Selection Rules from Generalized Discrete Gauging of Finite Non-Abelian Symmetries}},
author = {Hiroshi Ohki and Shohei Uemura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11895},
eprint = {2609.11895},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11895},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-invertible Selection Rules from Generalized Discrete Gauging of Finite Non-Abelian Symmetries
AU - Hiroshi Ohki
AU - Shohei Uemura
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.11895
UR - https://arxiv.org/abs/2609.11895
AB - We investigate non-invertible selection rules originating from the discrete H-gauging of theories with an underlying discrete global symmetry group G. To systematically describe these theories, we formulate a general framework for H-gauged models that incorporates generalized field transformations. Our approach naturally accommodates non-Abelian groups, for which multidimensional irreducible representations play an essential role. In such models with non-Abelian groups, the transformations induced by H non-trivially mix the internal components of G-multiplets, potentially projecting out specific degrees of freedom. Consequently, conventional selection rules based on standard tensor product decompositions or conjugacy classes become insufficient. By analyzing the full semidirect product G rtimes H, we introduce projected characters to derive necessary and sufficient conditions for non-vanishing n-point bare couplings. Furthermore, we demonstrate that the remaining field components obey an associative fusion-like algebra governed by their Clebsch-Gordan coefficients. Phenomenologically, these selection rules restrict allowed interactions and impose specific relations among coupling constants. We illustrate our results through concrete examples, including Δ(54) ≅ Δ(27)rtimes ℤ_2 and S_4 ≅ A_4 rtimes ℤ_2.
ER -