Title: Infinite index inclusions of von Neumann algebras and extensions in QFT
Speaker: Luca Giorgetti (University of Rome Tor Vergata)
Abstract: Subfactor theory provides a tool to study extensions in Quantum Field Theory (in the Algebraic QFT setting) and to construct new examples. The canonical situation is given by a field net of von Neumann algebras equipped with a global gauge action, extending its gauge invariant subnet (observable part of the theory). In the mathematical literature the main interest is on finite index subfactors. At the same time, finite index extensions are covered on the QFT side.
We report on a generalization of this analysis to the infinite index case (e.g. compact non-finite gauge groups) and show how QFTs with defects can be constructed. The main technical is tool is the notion of generalized Q-system (adapting Longo’s Q-systems to the infinite index setting) and the more special generalized Q-systems of intertwiners which characterize discrete inclusions among the semidiscrete ones (inclusions with a normal faithful conditional expectation). Joint work with Simone Del Vecchio (Roma, Tor Vergata) arXiv:1703.03605.