Comparing two approaches to the K-theory classification of D-branes

Details Comparing two approaches to the K-theory classification of D-branes Comparing two approaches to the K-theory classification of D-branes

2008-05-07

arxiv.org/abs/0805.1009v4

Journal of Geometry and Physics 61 (2011) pp. 191-212

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, no figures

Scientific paper

10.1016/j.geomphys.2010.10.001

We consider the two main classification methods of D-brane charges via K-theory, in type II superstring theory with vanishing B-field: the Gysin map approach and the one based on the Atiyah-Hirzebruch spectral sequence. Then, we find out an explicit link between these two approaches: the Gysin map provides a representative element of the equivalence class obtained via the spectral sequence. We also briefly discuss the case of rational coefficients, characterized by a complete equivalence between the two classification methods.

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