Classification of 2D Fermionic Systems with a $\mathbb Z_2$ Flavor Symmetry
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918438942801920 |
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| author | Chang, Chi-Ming Chen, Jin Xu, Fengjun |
| author_facet | Chang, Chi-Ming Chen, Jin Xu, Fengjun |
| contents | We classify superfusion categories describing two-dimensional fermionic systems equipped with the universal fermion-parity symmetry, implemented by a topological defect line (TDL) $Z$, and an additional $\mathbb{Z}_2$ flavor symmetry generated by a $W$ TDL. Depending on whether $W$ is m-type or q-type, its fusion rules lead to three distinct classes, and solving the super-pentagon equations yields 16 consistent superfusion categories. These are labeled by invariants $(ν_W,ν_Z,ν_{WZ})$, which determine the $\mathbb{Z}_8$ anomaly classes of the symmetries generated by $W$, $Z$, and $WZ$. We also provide explicit realizations using multiple Majorana fermions and comment on implications for fermionic CFTs and gapped phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09503 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of 2D Fermionic Systems with a $\mathbb Z_2$ Flavor Symmetry Chang, Chi-Ming Chen, Jin Xu, Fengjun High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics We classify superfusion categories describing two-dimensional fermionic systems equipped with the universal fermion-parity symmetry, implemented by a topological defect line (TDL) $Z$, and an additional $\mathbb{Z}_2$ flavor symmetry generated by a $W$ TDL. Depending on whether $W$ is m-type or q-type, its fusion rules lead to three distinct classes, and solving the super-pentagon equations yields 16 consistent superfusion categories. These are labeled by invariants $(ν_W,ν_Z,ν_{WZ})$, which determine the $\mathbb{Z}_8$ anomaly classes of the symmetries generated by $W$, $Z$, and $WZ$. We also provide explicit realizations using multiple Majorana fermions and comment on implications for fermionic CFTs and gapped phases. |
| title | Classification of 2D Fermionic Systems with a $\mathbb Z_2$ Flavor Symmetry |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2604.09503 |