Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916011715854336 |
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| author | Arias-Tamargo, Guillermo Smith, Philip Boyle Mouland, Rishi Hutt, Maxwell L. Velásquez Cotini |
| author_facet | Arias-Tamargo, Guillermo Smith, Philip Boyle Mouland, Rishi Hutt, Maxwell L. Velásquez Cotini |
| contents | We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form $\mathbb{Z}_k$ for each primitive Pythagorean triple $a^2 + b^2 = k^2$. The theory is self-dual under gauging any of these symmetries, and so to each there is associated a non-invertible topological defect. We study the properties of these lines, and show that any conformal boundary condition of two Dirac fermions that preserves a $U(1)^2$ symmetry can be found by dressing a trivial Dirichlet boundary with one of them. We discuss two microscopic descriptions of these defects: fermions coupled to a quantum-mechanical rotor degree of freedom; and an abelian gauge theory that realises symmetric mass generation in a half-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions Arias-Tamargo, Guillermo Smith, Philip Boyle Mouland, Rishi Hutt, Maxwell L. Velásquez Cotini High Energy Physics - Theory Strongly Correlated Electrons We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the form $\mathbb{Z}_k$ for each primitive Pythagorean triple $a^2 + b^2 = k^2$. The theory is self-dual under gauging any of these symmetries, and so to each there is associated a non-invertible topological defect. We study the properties of these lines, and show that any conformal boundary condition of two Dirac fermions that preserves a $U(1)^2$ symmetry can be found by dressing a trivial Dirichlet boundary with one of them. We discuss two microscopic descriptions of these defects: fermions coupled to a quantum-mechanical rotor degree of freedom; and an abelian gauge theory that realises symmetric mass generation in a half-space. |
| title | Non-Invertible Symmetries and Boundaries for Two-Dimensional Fermions |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.13952 |