The 3-permutation orbifold of a lattice vertex operator algebra

TL;DR

This paper explicitly classifies irreducible modules of a specific orbifold vertex operator algebra, computes their fusion rules via quantum dimensions, and provides the S-matrix, advancing understanding of its structure.

Contribution

It explicitly lists irreducible modules, determines fusion rules, and computes the S-matrix for the 3-permutation orbifold of a rank one lattice VOA, a novel detailed analysis.

Findings

Explicit classification of irreducible modules

Fusion rules determined by quantum dimensions

S-matrix explicitly computed

Abstract

Irreducible modules of the 3-permutation orbifold of a rank one lattice vertex operator algebra are listed explicitly. Fusion rules are determined by using the quantum dimensions. The $S$-matrix is also given.