Twisted Homology

Details Twisted Homology Twisted Homology

2006-11-20

arxiv.org/abs/hep-th/0611218v2

JHEP 0703:058,2007

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 3 eps figures, added Report-no

Scientific paper

10.1088/1126-6708/2007/03/058

D-branes are classified by twisted K-theory. Yet twisted K-theory is often hard to calculate. We argue that, in the case of a compactification on a simply-connected six manifold, twisted K-theory is isomorphic to a much simpler object, twisted homology. Unlike K-theory, homology can be twisted by a class of any degree and so it classifies not only D-branes but also M-branes. Twisted homology classes correspond to cycles in a certain bundle over spacetime, and branes may decay via Kachru-Pearson-Verlinde transitions only if this cycle is trivial. We provide a spectral sequence which calculates twisted homology, the kth step treats D(p-2k)-branes ending on Dp-branes.

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