An admissible level $\widehat{\mathfrak{osp}} \left( 1 \middle\vert 2 \right)$-model: modular transformations and the Verlinde formula
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866917813383331840 |
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| author | Ridout, David Snadden, John Wood, Simon |
| author_facet | Ridout, David Snadden, John Wood, Simon |
| contents | The modular properties of the simple vertex operator superalgebra associated to the affine Kac-Moody superalgebra $\widehat{\mathfrak{osp}} \left( 1 \middle\vert 2 \right)$ at level $-\frac{5}{4}$ are investigated. After classifying the relaxed highest-weight modules over this vertex operator superalgebra, the characters and supercharacters of the simple weight modules are computed and their modular transforms are determined. This leads to a complete list of the Grothendieck fusion rules by way of a continuous superalgebraic analogue of the Verlinde formula. All Grothendieck fusion coefficients are observed to be non-negative integers. These results indicate that the extension to general admissible levels will follow using the same methodology once the classification of relaxed highest-weight modules is completed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1705_04006 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | An admissible level $\widehat{\mathfrak{osp}} \left( 1 \middle\vert 2 \right)$-model: modular transformations and the Verlinde formula Ridout, David Snadden, John Wood, Simon High Energy Physics - Theory Mathematical Physics Quantum Algebra The modular properties of the simple vertex operator superalgebra associated to the affine Kac-Moody superalgebra $\widehat{\mathfrak{osp}} \left( 1 \middle\vert 2 \right)$ at level $-\frac{5}{4}$ are investigated. After classifying the relaxed highest-weight modules over this vertex operator superalgebra, the characters and supercharacters of the simple weight modules are computed and their modular transforms are determined. This leads to a complete list of the Grothendieck fusion rules by way of a continuous superalgebraic analogue of the Verlinde formula. All Grothendieck fusion coefficients are observed to be non-negative integers. These results indicate that the extension to general admissible levels will follow using the same methodology once the classification of relaxed highest-weight modules is completed. |
| title | An admissible level $\widehat{\mathfrak{osp}} \left( 1 \middle\vert 2 \right)$-model: modular transformations and the Verlinde formula |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/1705.04006 |