Discrete Torsion and Gerbes II
arXiv:hep-th/9909120
Abstract
In a previous paper we outlined how discrete torsion can be understood geometrically as an analogue of orbifold U(1) Wilson lines. In this paper we shall prove the remaining details. More precisely, in this paper we describe gerbes in terms of objects known as stacks (essentially, sheaves of categories), and develop much of the basic theory of gerbes in such language. Then, once the relevant technology has been described, we give a first-principles geometric derivation of discrete torsion. In other words, we define equivariant gerbes, and classify equivariant structures on gerbes and on gerbes with connection. We prove that in general, the set of equivariant structures on a gerbe with connection is a torsor under a group which includes H^2(G,U(1)), where G is the orbifold group. In special cases, such as trivial gerbes, the set of equivariant structures can furthermore be canonically identified with the group.
75 pages, must LaTeX 3x; v2: minor refinement in conclusions, other minor upgrades
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- Discrete Torsion and Branes in M-theory from Mathematical Viewpoint
- Forms on Vector Bundles Over Compact Real Hyperbolic Manifolds
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- Generalized Symmetries of Non-SUSY and Discrete Torsion String Backgrounds
- Quasi-quantum groups from Kalb-Ramond fields and magnetic amplitudes for strings on orbifolds
- BPS branes in discrete torsion orbifolds
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