Quantum dimensions and fusion rules of the VOA $ V^\tau_{L_{C \times D}}$

TL;DR

This paper computes quantum dimensions and fusion rules for a specific orbifold VOA and constructs certain subgroups within the automorphism group of a related holomorphic VOA, advancing understanding of VOA symmetries.

Contribution

It determines quantum dimensions and fusion rules for the orbifold code VOA and constructs 3-local subgroups in the automorphism group of a holomorphic VOA.

Findings

Quantum dimensions for the orbifold VOA are explicitly calculated.

Fusion rules for the orbifold VOA are established.

Construction of 3-local subgroups within the automorphism group of the holomorphic VOA.

Abstract

In this article, we determine quantum dimensions and fusion rules for the orbifold code VOA $ V^\tau_{L_{C \times D}}$. As an application, we also construct certain $3$-local subgroups inside the automorphism group of the VOA $V^\sharp$, where $V^\sharp$ is a holomorphic VOA obtained by the $\mathbb{Z}_3$-orbifold construction on the Leech lattice VOA.