Residual group-like symmetries in selection rules without group actions
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| Format: | Preprint |
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2026
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| author | Dong, Jun Kobayashi, Tatsuo Miyamoto, Shuhei Nishida, Ryusei Otsuka, Hajime |
| author_facet | Dong, Jun Kobayashi, Tatsuo Miyamoto, Shuhei Nishida, Ryusei Otsuka, Hajime |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14836 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Residual group-like symmetries in selection rules without group actions Dong, Jun Kobayashi, Tatsuo Miyamoto, Shuhei Nishida, Ryusei Otsuka, Hajime High Energy Physics - Theory High Energy Physics - Phenomenology 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. |
| title | Residual group-like symmetries in selection rules without group actions |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2603.14836 |