Presheaves of Superselection Structures in Curved Spacetimes

We show that superselection structures on curved spacetimes that are expected to describe quantum charges affected by the underlying geometry are categories of sections of presheaves of symmetric tensor categories. When an embedding functor is given, the superselection structure is a Tannaka-type dual of a locally constant group bundle, which hence becomes a natural candidate for the role of the gauge group. Indeed, we show that any locally constant group bundle (with suitable structure group) acts on a net of C* algebras fulfilling normal commutation relations on an arbitrary spacetime. We also give examples of gerbes of C* algebras, defined by Wightman fields and constructed using projective representations of the fundamental group of the spacetime, which we propose as solutions for the problem that existence and uniqueness of the embedding functor are not guaranteed.