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D-brane charge, flux quantisation and relative (co)homology

J. M. Figueroa-O'Farrill·S. Stanciu
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Abstract

We reconsider the problem of U(1) flux and D0-charge for D-branes in the WZW model and investigate the relationship between the different definitions that have been proposed recently. We identify the D0-charge as a particular reduction of a class in the relative cohomology of the group modulo the D-submanifold. We investigate under which conditions this class is equivalent to the first Chern class of a line bundle on the D-submanifold and we find that in general there is an obstruction given by the cohomology class of the NS 3-form. Therefore we conclude that for topologically nontrivial B-fields, there is strictly speaking no U(1) gauge field on the D-submanifold. Nevertheless the ambiguity in the flux is not detected by the D0-charge. This has a natural interpretation in terms of gerbes.

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J. M. Figueroa-O'Farrill, S. Stanciu. 2000-08-06. D-brane charge, flux quantisation and relative (co)homology. https://doi.org/10.1088/1126-6708%2F2001%2F01%2F006

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