2011/05/08 by T. Asselmeyer-Maluga, TORSTEN ASSELMEYER-MALUGA, J. Krol +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #gr-qc #hep-th #math-ph #math.GT #math.MP
paper · pdf · doi:10.1142/s0217751x11053857
published as Int. J. Mod. Phys. A 26 (2011) 3421-3437 · 18 pages, 1 figure
arxiv created 2011/05/08 · openalex publication_date 2011/07/14 · arxiv updated 2012/02/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 D p-branes as well to KK theory. These branes emerge when there are nontrivial NS–NS H-fluxes on S 3 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 D p-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.