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arXiv · 2210.11936

Orbifolds of Lattice Vertex Algebras

Bojko Bakalov·Jason Elsinger·Victor G. Kac·Ivan Todorov
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Abstract

To a positive-definite even lattice $Q$, one can associate the lattice vertex algebra $V_Q$, and any automorphism $\sigma$ of $Q$ lifts to an automorphism of $V_Q$. In this paper, we investigate the orbifold vertex algebra $V_Q^\sigma$, which consists of the elements of $V_Q$ fixed under $\sigma$, in the case when $\sigma$ has prime order. We describe explicitly the irreducible $V_Q^\sigma$-modules, compute their characters, and determine the modular transformations of characters. As an application, we find the asymptotic and quantum dimensions of all irreducible $V_Q^\sigma$-modules. We consider in detail the cases when the order of $\sigma$ is $2$ or $3$, as well as the case of permutation orbifolds.

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BibTeXRIS

Bojko Bakalov, Jason Elsinger, Victor G. Kac, Ivan Todorov. 2022-10-21. Orbifolds of Lattice Vertex Algebras. https://doi.org/10.1007/s11537-023-2249-7

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