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arXiv · 2603.14836

Residual group-like symmetries in selection rules without group actions

Jun Dong·Tatsuo Kobayashi·Shuhei Miyamoto·Ryusei Nishida·Hajime Otsuka
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Abstract

We analyze loop-induced group-like symmetries in theories where fields are labeled by basis elements of a fusion algebra constructed from the conjugacy classes of finite groups. Although the fusion rules for conjugacy classes are in general violated at loop level, residual group-like symmetries, including both Abelian and non-Abelian ones, remain exact through a procedure referred to as ``groupification''. By examining various conjugacy classes of finite groups realized in heterotic string theory on non-Abelian orbifolds, we identify an approximate discrete symmetry that controls the magnitude of loop-induced couplings. As a result, most parameters appearing in non-invertible selection rules are natural in the sense of 't Hooft. Furthermore, we discuss anomalies of the groupification symmetry, which can impose additional constraints on models with non-invertible fusion rules.

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Jun Dong, Tatsuo Kobayashi, Shuhei Miyamoto, Ryusei Nishida, Hajime Otsuka. 2026-03-16. Residual group-like symmetries in selection rules without group actions. https://arxiv.org/abs/2603.14836

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