Balanced root systems and a Schellekens-type list for holomorphic vertex operator algebras of central charge $32$

TL;DR

This paper investigates balanced holomorphic vertex operator algebras of central charge 32 and 40, establishing a key property about their Virasoro vectors and providing a classification list of potential root systems.

Contribution

It introduces the concept of balanced VOAs at these central charges and derives a Schellekens-type classification list for their root systems.

Findings

Virasoro vectors of balanced VOAs coincide with those of the subVOA generated by $V_1$

Provided a classification list of possible root systems for these VOAs

Established properties linking the structure of VOAs to their root systems

Abstract

We study a special class of holomorphic vertex operator algebras (VOAs) that we call \emph{balanced}.\ For a balanced, holomorphic VOA $V=\mathbb{C}\mathbf{1}\oplus V_1\oplus\dots$ with $c=32$ or $40$ we show that the Virasoro vectors of $V$ and the subVOA generated by $V_1$ coincide and use this result to provide a Schellekens-type list of possible root systems that may occur.