AG Mathematische Physik, Luca Giorgetti (Rom): Fusion category and hypergroup actions on conformal nets

Luca Giorgetti (Rom)

Fusion category and hypergroup actions on conformal nets

Abstract:

Groups
of automorphisms of a conformal net (the operator algebraic description
of chiral CFT) naturally give rise to subnets (subtheories), the
so-called group orbifolds. Moreover, automorphisms can be regarded as
the “ordinary” global symmetries in the conformal net setting. We
describe a generalization of these by means of unital completely
positive (UCP) maps of the net (a sort of “generalized” non-invertible
global symmetries of the net) obtained in a series of works in
collaboration with M. Bischoff and S. Del Vecchio.

In
the talk I will restrict to completely rational conformal nets, where
hypergroups of UCP maps (instead of groups of automorphisms) are capable
of describing arbitrary subnets of a given net. I will recall some
background of conformal nets, their representations, and report on some
new explicit formulas for such UCP actions, relating hypergroups of UCP
maps with certain unitary fusion category actions on conformal nets.