Holomorphic integer graded vertex superalgebras

TL;DR

This paper investigates holomorphic integer graded vertex superalgebras, establishing their properties at specific central charges and classifying possible structures of their weight-one Lie superalgebras.

Contribution

It proves that all such superalgebras with central charges 8 and 16 are purely even, and classifies the weight-one Lie superalgebras for central charge 24.

Findings

Superalgebras of central charge 8 and 16 are purely even.

For central charge 24, the weight-one Lie superalgebra is either zero, of superdimension 24, or in a list of 1332 semisimple Lie superalgebras.

Provides a classification of possible weight-one Lie superalgebras at central charge 24.

Abstract

In this note we study holomorphic integer graded vertex superalgebras. We prove that all such vertex superalgebras of central charge 8 and 16 are purely even. For the case of central charge 24 we prove that the weight-one Lie superalgebra is either zero, of superdimension 24, or else is one of an explicit list of 1332 semisimple Lie superalgebras.