Skip to main content
Article thumbnail
Location of Repository

D-branes, RR-fields and duality on noncommutative manifolds

By Jacek Brodzki, Varghese Mathai, Jonathan Rosenberg and Richard J. Szabo

Abstract

We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncom4 mutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant K-theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams

Topics: QA
Year: 2008
OAI identifier: oai:eprints.soton.ac.uk:49723
Provided by: e-Prints Soton

Suggested articles

Citations

  1. (2001). A.: Groups with the Haagerup property. Gromov’s a-T-menability. doi
  2. (1981). An analogue of the Thom isomorphism for crossed products of a C∗-algebra by an action of R.A d v .i nM a t h .39(1), doi
  3. (1997). Bivariante K-theorie für lokalconvexe Algebren und der bivariante
  4. (2004). Cyclic Theory and the Bivariant Chern character. In: doi
  5. (1978). Effros, E.G.: Nuclear C∗-algebras and the approximation property. doi
  6. (1969). Global theory of elliptic operators. In: doi
  7. (1996). Gravity coupled with matter and the foundation of noncommutative geometry. doi
  8. (1998). K-Theory for Operator Algebras, second edition. doi
  9. (1982). L.W.: Differential forms in algebraic topology. doi
  10. Loop Spaces, Characteristic Classes, and Geometric Quantization. doi
  11. (2002). Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples. doi
  12. (1994). Noncommutative Geometry. doi
  13. (2001). Noncommutative manifolds: The instanton algebra and isospectral deformations. doi
  14. (2004). On the topology and H-flux of T-dual manifolds. doi
  15. (1999). Periodic cyclic homology of certain nuclear algebras. doi
  16. (1980). R.G.: K homology and index theory. doi
  17. T-duality for principal torus bundles. doi
  18. (2004). T-duality: Topology change from H-flux. doi
  19. (1995). The Local Index Formula in Noncommutative Geometry. doi
  20. (1983). Théorie bivariante de Kasparov et opérateurs non bornés dans les C∗-modules hilbertiens.
  21. (2004). translation in Ukr.
  22. (2002). Twisted K-Theory and K-Theory of Bundle Gerbes. doi
  23. (2000). V.: D-Branes, B-Fields and Twisted K-Theory. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.