Orbifolds of Lattice Vertex Algebras
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866909058852716544 |
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| author | Bakalov, Bojko Elsinger, Jason Kac, Victor G. Todorov, Ivan |
| author_facet | Bakalov, Bojko Elsinger, Jason Kac, Victor G. Todorov, Ivan |
| contents | To a positive-definite even lattice $Q$, one can associate the lattice vertex algebra $V_Q$, and any automorphism $σ$ of $Q$ lifts to an automorphism of $V_Q$. In this paper, we investigate the orbifold vertex algebra $V_Q^σ$, which consists of the elements of $V_Q$ fixed under $σ$, in the case when $σ$ has prime order. We describe explicitly the irreducible $V_Q^σ$-modules, compute their characters, and determine the modular transformations of characters. As an application, we find the asymptotic and quantum dimensions of all irreducible $V_Q^σ$-modules. We consider in detail the cases when the order of $σ$ is $2$ or $3$, as well as the case of permutation orbifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11936 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orbifolds of Lattice Vertex Algebras Bakalov, Bojko Elsinger, Jason Kac, Victor G. Todorov, Ivan Quantum Algebra High Energy Physics - Theory Mathematical Physics Primary 17B69, Secondary 81R10 To a positive-definite even lattice $Q$, one can associate the lattice vertex algebra $V_Q$, and any automorphism $σ$ of $Q$ lifts to an automorphism of $V_Q$. In this paper, we investigate the orbifold vertex algebra $V_Q^σ$, which consists of the elements of $V_Q$ fixed under $σ$, in the case when $σ$ has prime order. We describe explicitly the irreducible $V_Q^σ$-modules, compute their characters, and determine the modular transformations of characters. As an application, we find the asymptotic and quantum dimensions of all irreducible $V_Q^σ$-modules. We consider in detail the cases when the order of $σ$ is $2$ or $3$, as well as the case of permutation orbifolds. |
| title | Orbifolds of Lattice Vertex Algebras |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Primary 17B69, Secondary 81R10 |
| url | https://arxiv.org/abs/2210.11936 |