The classification of vertex operator algebras of OZ-type generated by Ising vectors of σ-type

Abstract

We classify vertex operator algebras (VOAs) of OZ-type generated by Ising vectors of σ-type. As a consequence of the classification, we also prove that such VOAs are simple, rational, $C_2$-cofinite and unitary, that is, they have compact real forms generated by Ising vectors of σ-type over the real numbers.