2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51110In 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.To be published in the Proceedings of the Summer School "Geometric and Topological methods for Quantum Field Theory", Villa de Leyva, Colombia (2001)High Energy Physics - TheoryAlgebraic GeometryAlgebraic TopologyDifferential GeometryGeometric Topologytext