MATH Seminar

Title: Generalized Orbifolds in Conformal Field Theory
Seminar: Algebra
Speaker: Marcel Bischoff of Vanderbilt University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-09-20 at 4:00PM
Venue: W306
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Abstract: I will introduce the notion of a finite hypergroup. It turns out that certain subfactors (unital inclusions of von Neumann algebras with trivial center) can naturally be seen as such a fixed point. Chiral conformal field theory can be axiomatized as local conformal nets of von Neumann algebras.The orbifold of a conformal net is the fixed point with respect to a finite group of automorphisms. We define a generalized orbifold to be the fixed point of a conformal net under a proper hypergroup action. The fixed point is finite index subnet and it turns out that all finite index subnets are generalized orbifolds. A holomorphic conformal net is a conformal net with trivial representation category. For example, every positive even self-dual lattice gives such a conformal net. The representation category of a generalized orbifold of a holomorphic net is the Drinfeld center of a categorification of the hypergroup. Based on arXiv:1506.02606.