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

TL;DR

This paper proves that most holomorphic vertex operator superalgebras with central charge at most 24 are unitary and strongly graded-local, establishing their connection to conformal nets and classifying their properties.

Contribution

It demonstrates unitarity and strong graded-locality for nearly all such VOSAs with central charge up to 24, except for specific hypothetical cases.

Findings

Most holomorphic VOSAs with central charge ≤ 24 are unitary.

Majority of these VOSAs are strongly graded-local.

910 out of 969 VOSAs with central charge 24 are strongly graded-local.

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.