Research PapersNo Access
TOPOLOGICAL QUANTUM D-BRANES AND WILD EMBEDDINGS FROM EXOTIC SMOOTH ℝ4
https://doi.org/10.1142/S0217751X11053857Cited by:10 (Source: Crossref)
Abstract
This is the next step of uncovering the relation between string theory and exotic smooth ℝ4. Exotic smoothness of ℝ4 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 nontrivial NS–NS H-fluxes on S3 where the topological classes are determined by wild embeddings S2→S3. Then wild embeddings of higher dimensional p-complexes into Sn 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.
References
- Turkish J. Math. 20, 95 (1996). Web of Science, Google Scholar
- J. Gokova Geom. Topol. 2, 40 (2008), arXiv:0806.3010. Google Scholar
- J. Topology 2, 823 (2009), arXiv:0812.5098 DOI: 10.1112/jtopol/jtp025. Crossref, Web of Science, Google Scholar
J. W. Alexander ,Proceedings of the National Academy of Sciences of the United States 10 (1924) p. 8. Google Scholar- T. Asselmeyer-Maluga and J. Król, Quantum D-branes and exotic smooth ℝ4 , arXiv:1102.3274 . Google Scholar
- T. Asselmeyer-Maluga and J. Król, Gerbes on orbifolds and exotic smooth R4 , arXiv:0911.0271 . Google Scholar
- T. Asselmeyer-Maluga and J. Król, Abelian gerbes, generalized geometries and exotic R4 , arXiv:0904.1276 . Google Scholar
- T. Asselmeyer-Maluga and J. Król, Exotic smooth ℝ4, noncommutative algebras and quantization , arXiv:1001.0882 . Google Scholar
- , International Congress of Mathematicians ICM 2010 Short Communications Abstracts Book, ed.
R. Bathia (Hindustan Book Agency, 2010) p. 400. Google Scholar - T. Asselmeyer-Maluga and J. Król, Constructing a quantum field theory from spacetime , arXiv:1107.3458 . Google Scholar
- Int. J. Mod. Phys. A 26, 1375 (2011), arXiv:1101.3169. Link, Web of Science, ADS, Google Scholar
-
N. Berline , M. Vergne and E. Getzler , Heat Kernels and Dirac Operators ( Springer-Verlag , New York , 1992 ) . Crossref, Google Scholar - J. Diff. Geom. 39, 491 (1994). Crossref, Web of Science, Google Scholar
- J. Diff. Geom. 43, 458 (1996). Crossref, Web of Science, Google Scholar
- J. Math. Phys. 35, 5494 (1994), DOI: 10.1063/1.530761. Crossref, Web of Science, ADS, Google Scholar
- Gen. Relativ. Gravit. 25, 205 (1993), DOI: 10.1007/BF00758828. Crossref, Web of Science, ADS, Google Scholar
- Commun. Math. Phys. 277, 643 (2008), arXiv:hep-th/0607020 DOI: 10.1007/s00220-007-0396-y. Crossref, Web of Science, ADS, Google Scholar
- Bull. Amer. Math. Soc. 84, 832 (1978), DOI: 10.1090/S0002-9904-1978-14527-3. Crossref, Web of Science, Google Scholar
- Ann. Math. 110, 83 (1979), DOI: 10.2307/1971245. Crossref, Web of Science, Google Scholar
-
A. Casson ,Progress in Mathematics 62 ( Birkhäuser , 1986 ) . Google Scholar - Proc. Symp. Pure Math. 38, 521 (1984). Web of Science, Google Scholar
-
A. Connes , Noncommutative Geometry ( Academic Press , 1994 ) . Google Scholar - Inv. Math. 123, 343 (1997). Web of Science, ADS, Google Scholar
-
R. J. Daverman , Decompositions of Manifolds ( Academic Press , Orlando , 1986 ) . Google Scholar - J. Diff. Geom. 35, 219 (1992). Crossref, Web of Science, Google Scholar
-
S. Donaldson and P. Kronheimer , The Geometry of Four-Manifolds ( Oxford University Press , Oxford , 1990 ) . Crossref, Google Scholar - Topol. Appl. 31, 197 (1989), DOI: 10.1016/0166-8641(89)90082-5. Crossref, Web of Science, Google Scholar
- J. Diff. Geom. 17, 357 (1982). Crossref, Web of Science, Google Scholar
- Topology 23, 395 (1984), DOI: 10.1016/0040-9383(84)90002-8. Crossref, Web of Science, Google Scholar
- Topol. Appl. 32, 141 (1989), DOI: 10.1016/0166-8641(89)90051-5. Crossref, Web of Science, Google Scholar
-
R. E. Gompf and A. I. Stipsicz , 4-Manifolds and Kirby Calculus ( American Mathematical Society , 1999 ) . Crossref, Google Scholar - Ann. Math. 75, 452 (1962), DOI: 10.2307/1970208. Crossref, Web of Science, Google Scholar
- Adv. Theor. Math. Phys. 4, 127 (2000), arXiv:hep-th/9909089. Crossref, Google Scholar
-
J. Rosenberg , Algebraic K-Theory and its Application ( Springer , 1994 ) . Crossref, Google Scholar - Int. J. Mod. Phys. D 10, 311 (2001). Link, Web of Science, ADS, Google Scholar
-
I. Tamura , Topology of Foliations: An Introduction ,Translations of Math. Monographs 97 ( American Mathematical Society , Providence , 1992 ) . Google Scholar - Bull. Amer. Math. Soc. 78, 511 (1972), DOI: 10.1090/S0002-9904-1972-12975-6. Crossref, Web of Science, Google Scholar
- J. High Energy Phys. 9812, 019 (1998). ADS, Google Scholar
| You currently do not have access to the full text article. |
|---|
