Classification of holomorphic framed vertex operator algebras of central charge 24

TL;DR

This paper completes the classification of holomorphic framed vertex operator algebras with central charge 24, demonstrating they are uniquely determined by their weight one Lie algebra structure, identifying exactly 56 such algebras.

Contribution

It provides a complete classification of all holomorphic framed VOAs of central charge 24, showing they are uniquely identified by their weight one Lie algebra.

Findings

Exactly 56 such VOAs exist up to isomorphism

Each VOA is uniquely determined by its weight one Lie algebra

The classification confirms the structure of these VOAs is fully characterized by their Lie algebra

Abstract

This article is a continuation of our work on the classification of holomorphic framed vertex operator algebras of central charge 24. We show that a holomorphic framed VOA of central charge 24 is uniquely determined by the Lie algebra structure of its weight one subspace. As a consequence, we completely classify all holomorphic framed vertex operator algebras of central charge 24 and show that there exist exactly 56 such vertex operator algebras, up to isomorphism.