2006/07/31 by Jacek Brodzki, Varghese Mathai, Jonathan Rosenberg +1 · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.KT
paper · pdf · doi:10.1007/s00220-007-0396-y
published as Commun.Math.Phys.277:643-706,2008 · 56 pages; v3: final version, to appear in CMP
arxiv created 2007/06/26 · arxiv updated 2009/12/01
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.