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

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 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.

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

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Cited by in corpus (18)

• Twisted differential String and Fivebrane structures
• A worldsheet extension of O(d,d;Z)
• M/F-Theory as Mf-Theory
• Noncommutative gauge theories on D-branes in non-geometric backgrounds
• Spectral sequences in smooth generalized cohomology
• Groups with Spanier-Whitehead duality
• Topological quantum D-branes and wild embeddings from exotic smooth R^4
• Flux Quantization
• Topological T-Duality for Twisted Tori
• Index formulas and charge deficiencies on the Landau levels
• Noncommutative Geometry and Conformal Geometry. III. Vafa-Witten Inequality and Poincaré Duality
• Quantum D-branes and exotic smooth R^4
• Higher nonunital Quillen K'-theory, KK-dualities and applications to topological $\mathbb{T}$-dualities
• From geometry to non-geometry via T-duality
• Algebraic K-theory, K-regularity, and T-duality of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• KO-Homology and Type I String Theory
• Stratified Fiber Bundles, Quinn Homology and Brane Stability of Hyperbolic Orbifolds
• D-branes, KK-theory and duality on noncommutative spaces