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