Title: Deligne Cohomology for Orbifolds, discrete torsion and B-fields
Abstract:In this paper we introduce the concept of Deligne cohomology of an orbifold. We prove that the third Deligne cohomology group of a smooth étale groupoid classify gerbes with connection over the groupo...In this paper we introduce the concept of Deligne cohomology of an orbifold. We prove that the third Deligne cohomology group of a smooth étale groupoid classify gerbes with connection over the groupoid. We argue that the $B$-field and the discrete torsion in type II superstring theories are special kinds of gerbes with connection, and finally, for each one of them, using Deligne cohomology we construct a flat line bundle over the inertia groupoid, namely a Ruan inner local in the case of an orbifold.Read More