Haploid algebras in $C^*$-tensor categories and the Schellekens list
| Autor: | Sebastiano Carpi, Tiziano Gaudio, Luca Giorgetti, Robin Hillier |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
High Energy Physics - Theory
Mathematics - Operator Algebras FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Settore MAT/02 High Energy Physics - Theory (hep-th) Settore MAT/07 Settore MAT/05 Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Operator Algebras (math.OA) Mathematical Physics |
| Popis: | We prove that a haploid associative algebra in a $C^*$-tensor category $\mathcal{C}$ is equivalent to a Q-system (a special $C^*$-Frobenius algebra) in $\mathcal{C}$ if and only if it is rigid. This allows us to prove the unitarity of all the 70 strongly rational holomorphic vertex operator algebras with central charge $c=24$ and non-zero weight-one subspace, corresponding to entries 1-70 of the so called Schellekens list. Furthermore, using the recent generalized deep hole construction of these vertex operator algebras, we prove that they are also strongly local in the sense of Carpi, Kawahigashi, Longo and Weiner and consequently we obtain some new holomorphic conformal nets associated to the entries of the list. Finally, we completely classify the simple CFT type vertex operator superalgebra extensions of the unitary $N=1$ and $N=2$ super-Virasoro vertex operator superalgebras with central charge $c 44 pages, revised version |
| Databáze: | OpenAIRE |
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