Deligne Cohomology for Orbifolds, discrete torsion and B-fields

Ernesto Lupercio; Bernardo Uribe

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arXiv · hep-th/0201184

Deligne Cohomology for Orbifolds, discrete torsion and B-fields

Ernesto Lupercio·Bernardo Uribe

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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 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.

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Ernesto Lupercio, Bernardo Uribe. 2002-04-25. Deligne Cohomology for Orbifolds, discrete torsion and B-fields. https://arxiv.org/abs/hep-th/0201184

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