Most vertex superalgebras associated to an odd unimodular lattice of rank 24 have an N=4 superconformal structure

TL;DR

This paper demonstrates that most vertex superalgebras derived from odd unimodular lattices of rank 24 contain an N=4 superconformal subalgebra, revealing a common superconformal structure in these mathematical objects.

Contribution

It establishes that at least 267 out of 273 such vertex superalgebras have an embedded N=4 superconformal algebra, a new insight into their structure.

Findings

At least 267 of the 273 lattices' vertex superalgebras contain an N=4 superconformal subalgebra.

The embedding is shown via studying lattice embeddings of rank 6.

Most vertex superalgebras associated to these lattices have an N=4 structure.

Abstract

Odd, positive-definite, integral, unimodular lattices N of rank 24 were classified by Borcherds. There are 273 isometry classes of such lattices. Associated to them are vertex superalgebras $V_N$ of central charge c=24. We show that at least 267 of these vertex operator superalgebras contain an N=4 superconformal subalgebra of central charge $c'=6$. This is achieved by studying embeddings $L+\subseteq N$ of a certain rank 6 lattice L+.