Every conformal net has an associated unitary VOA
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908586178772992 |
|---|---|
| author | Henriques, André G. Tener, James E. |
| author_facet | Henriques, André G. Tener, James E. |
| contents | Unitary vertex operator algebras (VOAs) and conformal nets are the two most prominent mathematical axiomatizations of two-dimensional unitary chiral conformal field theories. They are conjectured to be equivalent, but a rigorous comparison has proven challenging. We resolve one direction of the conjecture by showing that every conformal net has an associated unitary VOA. We also show that every representation of a conformal net in which the generator of rotation acts with discrete spectrum and finite-dimensional eigenspaces yields a unitary module of the corresponding VOA. A talk describing our results is available at: https://www.youtube.com/watch?v=f_LhNSeiiaE . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Every conformal net has an associated unitary VOA Henriques, André G. Tener, James E. Operator Algebras Mathematical Physics Quantum Algebra 46L60 17B69 81T40 81T05 Unitary vertex operator algebras (VOAs) and conformal nets are the two most prominent mathematical axiomatizations of two-dimensional unitary chiral conformal field theories. They are conjectured to be equivalent, but a rigorous comparison has proven challenging. We resolve one direction of the conjecture by showing that every conformal net has an associated unitary VOA. We also show that every representation of a conformal net in which the generator of rotation acts with discrete spectrum and finite-dimensional eigenspaces yields a unitary module of the corresponding VOA. A talk describing our results is available at: https://www.youtube.com/watch?v=f_LhNSeiiaE . |
| title | Every conformal net has an associated unitary VOA |
| topic | Operator Algebras Mathematical Physics Quantum Algebra 46L60 17B69 81T40 81T05 |
| url | https://arxiv.org/abs/2507.20735 |