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

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

2006-07-04

arxiv.org/abs/hep-th/0607020v3

Commun.Math.Phys.277:643-706,2008

Physics

High Energy Physics

High Energy Physics - Theory

56 pages; v3: final version, to appear in CMP

Scientific paper

10.1007/s00220-007-0396-y

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 Poincare 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.

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