Infinite index extensions of local nets and defects

Abstract

Subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [LR95] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (non-finite) group of internal symmetries. Building on the works of Izumi, Longo, Popa [ILP98] and Fidaleo, Isola [FI99], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [Lon94] to the infinite index case. We characterize inclusions which admit generalized Q-systems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [BKLR16].Comment: 50 page

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

“…In the conformal net setting there are various abstract results on the general structure of conformal subnets, see e.g. [1,9,13,41,49,50,57] but it is not clear how to use them in order to get explicit classification results in concrete models. For example it has been shown in [1] that the finite index subnets of a given net can be completely described in terms of hypergroup actions but it is not clear how to determine the structure of these hypergroup actions without knowing the subnet structure a priori.…”