Toward classfication of rational vertex operator algebras with central charges less than 1

TL;DR

This paper classifies rational, C_2-cofinite simple vertex operator algebras with central charges less than 1, revealing their structure and extensions related to Virasoro algebras, and establishing simplicity of certain subalgebras.

Contribution

It provides a complete classification of such vertex operator algebras with equal effective and central charges below 1, including their structure and subalgebra properties.

Findings

Zero algebra for c<0

Unique structure for c=0

Extensions of Virasoro VOAs for c>0

Abstract

The rational and C_2-cofinite simple vertex operator algebras whose effective central charges and the central charges c are equal and less than 1 are classified. Such a vertex operator algebra is zero if c<0 and C if c=0. If c>0, it is an extension of discrete Virasoro vertex operator algebra L(c_{p,q},0) by its irreducible modules. It is also proved that for any rational and C_2-cofinite simple vertex operator algebra whose effective central charge and central charge are equal, the vertex operator subalgebra generated by the Virasoro vector is simple.