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Communications in Mathematical Physics

, Volume 277, Issue 3, pp 643–706 | Cite as

D-Branes, RR-Fields and Duality on Noncommutative Manifolds

  • Jacek Brodzki
  • Varghese MathaiEmail author
  • Jonathan Rosenberg
  • Richard J. Szabo
Article

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 noncommutative 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 \(\mathsf K\)-theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.

Keywords

Chern Character Cyclic Homology Fundamental Class Spectral Triple Cyclic Cohomology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Jacek Brodzki
    • 1
  • Varghese Mathai
    • 2
    Email author
  • Jonathan Rosenberg
    • 3
  • Richard J. Szabo
    • 4
  1. 1.School of MathematicsUniversity of SouthamptonSouthamptonUK
  2. 2.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia
  3. 3.Department of MathematicsUniversity of MarylandCollege ParkUSA
  4. 4.Department of Mathematics and Maxwell Institute for Mathematical SciencesHeriot-Watt UniversityRiccarton, EdinburghUK

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