Year: 2020
Type: article
Abstract: We introduce a simple, self-dual, rational, and $C_2$-cofinite vertex operator algebra of CFT-type associated with a $\mathbb{Z}_k$-code for $k \ge 2$. Our argument is based on the $\mathbb{Z}_k$-symmetry among the simple current modules for the parafermion vertex operator algebra $K(\mathfrak{sl}_2, k)$. 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.
Authors: Tomoyuki ARAKAWA, Hiromichi YAMADA, Hiroshi YAMAUCHI
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: Vertex algebras and 4-dimensional supersymmetric quantum field theories, Deepening the theory of vertex algebras by international joint researches, W代数とその応用, Chiral algebras of class S and symplectic geometry, Research on construction of vertex operator algebras based on tensor categories and their symmeties
OpenAlex ID: W2963967852