D-brane charge, flux quantisation and relative (co)homology
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.
Cite
@article{arxiv.hep-th/0008038,
title = {D-brane charge, flux quantisation and relative (co)homology},
author = {J. M. Figueroa-O'Farrill and S. Stanciu},
journal= {arXiv preprint arXiv:hep-th/0008038},
year = {2009}
}
Comments
16 pages, 3 figures (v2: cosmetic changes and definition of relative de Rham complex)