Fermionic Non-invertible Symmetry Behind Supersymmetric ADE Solitons
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909928767094784 |
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| author | Chen, Jin Duan, Zhihao Jia, Qiang Lee, Sungjay |
| author_facet | Chen, Jin Duan, Zhihao Jia, Qiang Lee, Sungjay |
| contents | The non-perturbative constraints imposed by intrinsic fermionic non-invertible symmetries in 1+1 dimensional gapped systems remain largely unexplored. In this letter, we propose the superstrip algebra as a unified framework to catalog the categorical symmetry data in a massive fermionic model. The algebra and its representations explicitly encode the vacuum structure, soliton degeneracies, and their quantum numbers. As a demonstration, we apply this framework to the $\mathcal N=2$ minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of $\text{SU}(2)_k$ known to underlie the $ADE$ classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting $ADE$-type soliton spectrum and their fractional fermion number. Although our primary examples are supersymmetric and integrable, our framework itself relies on neither property, providing a new powerful tool for studying a broad class of strongly-coupled fermionic systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_22129 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fermionic Non-invertible Symmetry Behind Supersymmetric ADE Solitons Chen, Jin Duan, Zhihao Jia, Qiang Lee, Sungjay High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics The non-perturbative constraints imposed by intrinsic fermionic non-invertible symmetries in 1+1 dimensional gapped systems remain largely unexplored. In this letter, we propose the superstrip algebra as a unified framework to catalog the categorical symmetry data in a massive fermionic model. The algebra and its representations explicitly encode the vacuum structure, soliton degeneracies, and their quantum numbers. As a demonstration, we apply this framework to the $\mathcal N=2$ minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of $\text{SU}(2)_k$ known to underlie the $ADE$ classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting $ADE$-type soliton spectrum and their fractional fermion number. Although our primary examples are supersymmetric and integrable, our framework itself relies on neither property, providing a new powerful tool for studying a broad class of strongly-coupled fermionic systems. |
| title | Fermionic Non-invertible Symmetry Behind Supersymmetric ADE Solitons |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2511.22129 |