The balanced structure on the category of representations of a conformal net
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914578308268032 |
|---|---|
| author | Marín-Salvador, Adrià |
| author_facet | Marín-Salvador, Adrià |
| contents | Let $\mathcal{A}$ be a (not necessarily rational) conformal net. We show that the braided $\mathrm{W}^*$-tensor category $\text{Rep}(\mathcal{A})$ of representations of $\mathcal{A}$ is canonically a balanced $\mathrm{W}^*$-tensor category. The balance is given by the action of $e^{-2πi L_0}$, where $L_0$ denotes the generator of rotations on $S^1$. In future work, we generalize this result to the larger context of a group acting on $\mathcal{A}$. We provide here a more accessible proof for the case where no group is present. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18446 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The balanced structure on the category of representations of a conformal net Marín-Salvador, Adrià Quantum Algebra Mathematical Physics Operator Algebras 81T40 Let $\mathcal{A}$ be a (not necessarily rational) conformal net. We show that the braided $\mathrm{W}^*$-tensor category $\text{Rep}(\mathcal{A})$ of representations of $\mathcal{A}$ is canonically a balanced $\mathrm{W}^*$-tensor category. The balance is given by the action of $e^{-2πi L_0}$, where $L_0$ denotes the generator of rotations on $S^1$. In future work, we generalize this result to the larger context of a group acting on $\mathcal{A}$. We provide here a more accessible proof for the case where no group is present. |
| title | The balanced structure on the category of representations of a conformal net |
| topic | Quantum Algebra Mathematical Physics Operator Algebras 81T40 |
| url | https://arxiv.org/abs/2605.18446 |