The classification of vertex operator algebras of OZ-type generated by Ising vectors of $\sigma$-type

TL;DR

This paper classifies a specific class of vertex operator algebras generated by Ising vectors of $\sigma$-type, establishing their structural properties and unitarity, which advances understanding in algebraic and conformal field theory contexts.

Contribution

It provides a complete classification of OZ-type VOAs generated by Ising vectors of $\sigma$-type and proves their simplicity, rationality, $C_2$-cofiniteness, and unitarity.

Findings

VOAs are simple and rational

VOAs are $C_2$-cofinite and unitary

Existence of compact real forms generated by Ising vectors

Abstract

We classify vertex operator algebras (VOAs) of OZ-type generated by Ising vectors of $\sigma$-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 $\sigma$-type over the real numbers.