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

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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.

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Authors and Affiliations

  1. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

    Jacek Brodzki

  2. Department of Pure Mathematics, University of Adelaide, Adelaide, 5005, Australia

    Varghese Mathai

  3. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Jonathan Rosenberg

  4. Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, UK

    Richard J. Szabo

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  1. Jacek Brodzki
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  2. Varghese Mathai
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  3. Jonathan Rosenberg
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  4. Richard J. Szabo
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Correspondence to Varghese Mathai.

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Communicated by A. Connes

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Brodzki, J., Mathai, V., Rosenberg, J. et al. D-Branes, RR-Fields and Duality on Noncommutative Manifolds. Commun. Math. Phys. 277, 643–706 (2008). https://doi.org/10.1007/s00220-007-0396-y

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