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

Infinite index extensions of local nets and defects