On dimensions of (2+1)D abelian bosonic topological systems on non-orientable manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908773655773184 |
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| author | Orii, Ippo |
| author_facet | Orii, Ippo |
| contents | We give a framework to describe abelian bosonic topological systems with parity symmetry on a torus in terms of the projective representation of $GL(2,\mathbb{Z})$. However, this information alone does not guarantee that we can assign Hilbert spaces to non-orientable surfaces in a way compatible with the gluing axiom of topological quantum field theory. Here, we show that we may assign Hilbert spaces with integer dimensions to non-orientable surfaces in the case of abelian bosonic topological systems with time-reversal symmetry, which can be seen as a necessary condition for the existence of topological quantum field theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On dimensions of (2+1)D abelian bosonic topological systems on non-orientable manifolds Orii, Ippo High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics We give a framework to describe abelian bosonic topological systems with parity symmetry on a torus in terms of the projective representation of $GL(2,\mathbb{Z})$. However, this information alone does not guarantee that we can assign Hilbert spaces to non-orientable surfaces in a way compatible with the gluing axiom of topological quantum field theory. Here, we show that we may assign Hilbert spaces with integer dimensions to non-orientable surfaces in the case of abelian bosonic topological systems with time-reversal symmetry, which can be seen as a necessary condition for the existence of topological quantum field theories. |
| title | On dimensions of (2+1)D abelian bosonic topological systems on non-orientable manifolds |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2502.13532 |