Orbifolds of lattice vertex algebras

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 prim...

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Bibliographic Details
Published in:Japanese journal of mathematics 2023-09, Vol.18 (2), p.169-274
Main Authors: Bakalov, Bojko, Elsinger, Jason, Kac, Victor G., Todorov, Ivan
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
History of Mathematical Sciences
Lattices (mathematics)
Mathematics
Mathematics and Statistics
Modules
Permutations
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Summary: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.
ISSN:0289-2316
1861-3624
DOI:10.1007/s11537-023-2249-7