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].

50 pages

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Cited by in corpus (6)

• Compact Hypergroups from Discrete Subfactors
• Galois Correspondence and Fourier Analysis on Local Discrete Subfactors
• Quantum Operations on Conformal Nets
• Wightman fields for two-dimensional conformal field theories with pointed representation category
• Classification of unitary vertex subalgebras and conformal subnets for rank-one lattice chiral CFT models
• A planar algebraic description of conditional expectations