Topological quantum D-branes and wild embeddings from exotic smooth
May, 2011Citations per year
Abstract: (arXiv)
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 -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.Note:
- 18 pages, 1 figure
- Quantum D-branes
- wild embeddings
- noncommutative geometry
- exotic R4
- approximation: classical
- homology: sphere
- geometry: noncommutative
- operator: Dirac
- algebra: von Neumann
- K-theory
References(25)
Figures(1)