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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Quantenfeldtheorie II

MP 11.1: Talk

Wednesday, March 18, 2015, 15:45–16:05, HFT-FT 101

DHR categories and reconstruction of local nets — •Luca Giorgetti — Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

Rational chiral conformal field theories are described by local nets of algebras on the line in the axiomatic language of AQFT. Their representation theory (superselection sectors) can as well be translated into algebra by means of the corresponding category of DHR endomorphisms. These categories all share the structure of abstract braided C* tensor categories and, in this sense, it is known that non isomorphic models can yield equivalent categories. We investigate the problem of making the correspondence 1:1 by adding on top of the DHR category its action on the global algebra of observables, and we show duality relations between local algebras and localized endomorphisms pointing in this direction. We ask if every (modular) braided C* tensor category is realized as DHR category of some (rational) net of algebras.