Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models

TL;DR

This paper classifies all unitary subalgebras of rank-one lattice vertex operator algebras and their corresponding conformal subnets, advancing understanding of their algebraic and conformal structures.

Contribution

It provides a complete classification of subalgebras and subnets for even rank-one lattice models, linking vertex operator algebras and conformal nets.

Findings

Complete classification of subalgebras of rank-one lattice VOAs

Corresponding classification of conformal subnets

Establishment of a correspondence between VOAs and conformal nets

Abstract

We provide a complete classification of unitary subalgebras of even rank-one lattice vertex operator algebras. As a consequence of the correspondence between vertex operator algebras and conformal nets, we also obtain a complete classification of conformal subnets of even rank-one lattice conformal nets.