# Infinite index extensions of local nets and defects

## TL;DR

This paper extends subfactor theory to infinite index cases in quantum field theory, enabling the construction of models with defects and phase boundaries related to non-finite symmetry groups.

## Contribution

It generalizes the concept of Q-systems to infinite index inclusions, allowing the analysis and construction of new quantum field theory models with defects.

## Key findings

- Characterization of inclusions admitting generalized Q-systems
- Definition of a braided product for these Q-systems
- Construction of QFT models with infinite index 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].