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

2018/09/29 by Höhn, Gerald, Mason, Geoffrey
#17B69 #17B81 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1810.00254

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+⊆ N of a certain rank 6 lattice L+.

Related

• N=2 and N=4 Subalgebras of Super Vertex Operator Algebras
• Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24
• Holomorphic integer graded vertex superalgebras
• Self-Dual Vertex Operator Superalgebras of Large Minimal Weight
• Holomorphic Vertex Operator Algebras of Small Central Charges