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arXiv · 2211.15952

Unitary forms for holomorphic vertex operator algebras of central charge $24$

Ching Hung Lam
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Abstract

We prove that all holomorphic vertex operator algebras of central charge $24$ with non-trivial weight one subspaces are unitary. The main method is to use the orbifold construction of a holomorphic VOA $V$ of central charge $24$ directly from a Niemeier lattice VOA $V_N$. We show that it is possible to extend the unitary form for the lattice VOA $V_N$ to the holomorphic VOA $V$ by using the orbifold construction and some information of the automorphism group $\mathrm{Aut}(V)$.

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Ching Hung Lam. 2022-11-29. Unitary forms for holomorphic vertex operator algebras of central charge $24$. https://doi.org/10.1007/s11005-023-01652-4

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