# Presheaves of superselection structures in curved spacetimes

November 08, 2012

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. This
implies that, provided an embedding functor (whose existence and uniqueness are
not guaranteed), the superselection structure is a Tannaka-type dual of a
locally constant group bundle, which hence becomes a natural candidate for the
role of 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.

Keywords:

Superselection Theory, QFT on curved spacetimes