ℤ_𝑘-code vertex operator algebras

Abstract

We introduce a simple, self-dual, rational, and 𝐶₂-cofinite vertex operator algebra of CFT-type associated with a ℤ_𝑘-code for 𝑘 ≥ 2. Our argument is based on the ℤ_𝑘-symmetry among the simple current modules for the parafermion vertex operator algebra 𝐾(𝔰𝔩₂, 𝑘). We show that it is naturally realized as the commutant of a certain subalgebra in a lattice vertex operator algebra. Furthermore, we construct all the irreducible modules inside a module for the lattice vertex operator algebra.