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

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

Research output: Contribution to journalArticle

29 Citations (Scopus)

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 K -theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams. © 2007 Springer-Verlag.

Original languageEnglish
Pages (from-to)643-706
Number of pages64
JournalCommunications in Mathematical Physics
Volume277
Issue number3
DOIs
Publication statusPublished - Feb 2008

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