2025/05/06 by Bin Gui, Gui, Bin · 1 citation
Computer Science · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2505.03235
openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
Let V be one of the following unitary strongly-rational VOAs: unitary WZW models, discrete series W-algebras of type ADE, even lattice VOAs, parafermion VOAs, their tensor products, and their strongly-rational cosets. Let U be a (unitary) VOA extension of V, described by a Q-system Q. We prove that U is strongly local. Let \mathcal AV,\mathcal AU be the conformal nets associated to V,U in the sense of Carpi-Kawahigashi-Longo-Weiner (CKLW). We prove that \mathcal AU is canonically isomorphic to the conformal net extension of \mathcal AV defined by the Q-system Q. We prove that all unitary U-modules are strongly integrable in the sense of Carpi-Weiner-Xu (CWX). We show that the CWX *-functor from the C^*-category of unitary U-modules to the C^*-category of finite-index \mathcal AU-modules is naturally isomorphic to *-functor defined by Q.