Topological quantum D-branes and wild embeddings from exotic smooth R^4

Details Topological quantum D-branes and wild embeddings from exotic smooth R^4 Topological quantum D-branes and wild embeddings from exotic smooth R^4

2011-05-08

arxiv.org/abs/1105.1557v1

Int. J. Mod. Phys. A 26 (2011) 3421-3437

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 1 figure

Scientific paper

10.1142/S0217751X11053857

This is the next step of uncovering the relation between string theory and exotic smooth R^4. Exotic smoothness of R^4 is correlated with D6 brane charges in IIA string theory. We construct wild embeddings of spheres and relate them to a class of topological quantum Dp-branes as well to KK theory. These branes emerge when there are non-trivial NS-NS H-fluxes where the topological classes are determined by wild embeddings S^2 -> S^3. Then wild embeddings of higher dimensional $p$-complexes into S^n correspond to Dp-branes. These wild embeddings as constructed by using gropes are basic objects to understand exotic smoothness as well Casson handles. Next we build C*-algebras corresponding to the embeddings. Finally we consider topological quantum D-branes as those which emerge from wild embeddings in question. We construct an action for these quantum D-branes and show that the classical limit agrees with the Born-Infeld action such that flat branes = usual embeddings.

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