Infinite index extensions of local nets and defects

Simone Del Vecchio, Luca Giorgetti
March 10, 2017
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].
open access link Rev. Math. Phys. 30 (2018) 1850002
@article{DelVecchio:2017axj, author = "Del Vecchio, Simone and Giorgetti, Luca", title = "{Infinite index extensions of local nets and defects}", journal = "Rev. Math. Phys.", volume = "30", year = "2017", number = "02", pages = "1850002", doi = "10.1142/S0129055X18500022", note = "[Rev. Math. Phys.30,0002(2018)]", eprint = "1703.03605", archivePrefix = "arXiv", primaryClass = "math.OA", SLACcitation = "%%CITATION = ARXIV:1703.03605;%%" }