Lattice subalgebras of strongly regular vertex operator algebras

TL;DR

This paper proves a strengthened version of a conjecture regarding lattice subalgebras in strongly regular vertex operator algebras, leading to new structural insights and generalizations in the theory.

Contribution

It provides a sharpened proof of a conjecture on lattice subalgebras and introduces applications including a canonical conformal subVOA and a generalization of minimal models.

Findings

Existence of a canonical conformal subVOA W⊗G⊗Z within V

Generalization of the theory of minimal models

Enhanced understanding of lattice subalgebras in strongly regular VOAs

Abstract

We prove a sharpened version of a conjecture of Dong-Mason about lattice subalgebras of a strongly regular vertex operator algebra $V$, and give some applications. These include the existence of a canonical conformal subVOA $W\otimes G\otimes Z \subseteq V$, and a generalization of the theory of minimal models.