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arXiv · 2410.07099

Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24

Tiziano Gaudio
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Abstract

We prove that all nice holomorphic vertex operator superalgebras (VOSAs) with central charge at most 24 and with non-trivial odd part are unitary, apart from the hypothetical ones arising as fake copies of the shorter moonshine VOSA or of the latter tensorized with a real free fermion VOSA. Furthermore, excluding the ones with central charge 24 of glueing type III and with no real free fermion, we show that they are all strongly graded-local. In particular, they naturally give rise to holomorphic graded-local conformal nets. In total, we are able to prove that 910 of the 969 nice holomorphic VOSAs with central charge 24 and with non-trivial odd part are strongly graded-local, without counting hypothetical fake copies of the shorter moonshine VOSA tensorized with a real free fermion VOSA.

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BibTeXRIS

Tiziano Gaudio. 2024-10-09. Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24. https://doi.org/10.1007/s00023-025-01542-6

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