Most Vertex Superalgebras Associated to an Odd Unimodular Lattice of Rank 24 Have an Superconformal Structure

  title={Most Vertex Superalgebras Associated to an Odd Unimodular Lattice of Rank 24 Have an Superconformal Structure},
  author={Gerald Hohn and Geoffrey Mason},
  journal={Experimental Mathematics},
  • G. Hohn, G. Mason
  • Published 29 September 2018
  • Mathematics
  • Experimental Mathematics
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+. 
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