Berlin 2014 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: Quantenfeldtheorie III

MP 10.3: Talk

Thursday, March 20, 2014, 15:20–15:40, SPA SR125

Characterisation of local nets by their representation category — •Luca Giorgetti — Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany

In the axiomatic setting of Haag and Kastler, quantum fields are described by local nets of bounded operator algebras over space-time regions. We will discuss the representation theory of the net, more specifically the DHR superselection sectors of two-dimensional conformal field theories. These admit at the same time a large number of non-trivial models and a rich representation theoretical structure. DHR representations form a braided (modular) tensor category which we conjecture to be uniquely determined by a finite set of numerical invariants ('modular data'). Moreover, the category is realised in our setting as endomorphisms of the net. Based on our present understanding of the problem, we discuss to which extent one can reconstruct the local algebras from the category, together with its action on the net.