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arXiv · hep-th/0611218

Twisted Homology

Andres Collinucci·Jarah Evslin
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Abstract

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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Andres Collinucci, Jarah Evslin. 2006-11-22. Twisted Homology. https://doi.org/10.1088/1126-6708%2F2007%2F03%2F058

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