Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912503487791104 |
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| author | Kawabata, Kohki Nishioka, Tatsuma Okuda, Takuya Yahagi, Shinichiro |
| author_facet | Kawabata, Kohki Nishioka, Tatsuma Okuda, Takuya Yahagi, Shinichiro |
| contents | A quantum field theory is referred to as bosonic (non-spin) if its physical quantities are independent of the spacetime spin structure, and as fermionic (spin) if they depend on it. We explore fermionic conformal field theories (CFTs) that emerge from bosonic abelian Chern-Simons theories, playing the role of a symmetry topological field theory, by imposing topological boundary conditions. Our construction includes the fermionic generalization of code CFTs. When the Chern-Simons theory is associated with the root lattice of a simply laced Lie algebra, this approach yields a fermionic CFT with a level-one affine Lie algebra symmetry. As an application, we consider the Chern-Simons theories corresponding to a class of supersymmetric vertex operator algebras studied by Johnson-Freyd and classify their fermionic topological boundary conditions that give rise to supersymmetric CFTs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08084 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fermionic CFTs from topological boundaries in abelian Chern-Simons theories Kawabata, Kohki Nishioka, Tatsuma Okuda, Takuya Yahagi, Shinichiro High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics A quantum field theory is referred to as bosonic (non-spin) if its physical quantities are independent of the spacetime spin structure, and as fermionic (spin) if they depend on it. We explore fermionic conformal field theories (CFTs) that emerge from bosonic abelian Chern-Simons theories, playing the role of a symmetry topological field theory, by imposing topological boundary conditions. Our construction includes the fermionic generalization of code CFTs. When the Chern-Simons theory is associated with the root lattice of a simply laced Lie algebra, this approach yields a fermionic CFT with a level-one affine Lie algebra symmetry. As an application, we consider the Chern-Simons theories corresponding to a class of supersymmetric vertex operator algebras studied by Johnson-Freyd and classify their fermionic topological boundary conditions that give rise to supersymmetric CFTs. |
| title | Fermionic CFTs from topological boundaries in abelian Chern-Simons theories |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2502.08084 |