# Infinite index extensions of local nets and defects

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;%%"
}

Keywords:

*none*