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

D-branes, RR-fields and duality on noncommutative manifolds
D-branes, RR-fields and duality on noncommutative manifolds
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 noncom4 mutative 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.
0010-3616
643-706
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Mathai, Varghese
70efa223-e5cc-4942-9d44-ad23023b1efa
Rosenberg, Jonathan
c1dbabea-cfa2-4b65-85a8-7e51fe5b9054
Szabo, Richard J.
c852e73d-9c9f-4b65-afaa-69411a151f09
Brodzki, Jacek
b1fe25fd-5451-4fd0-b24b-c59b75710543
Mathai, Varghese
70efa223-e5cc-4942-9d44-ad23023b1efa
Rosenberg, Jonathan
c1dbabea-cfa2-4b65-85a8-7e51fe5b9054
Szabo, Richard J.
c852e73d-9c9f-4b65-afaa-69411a151f09

Brodzki, Jacek, Mathai, Varghese, Rosenberg, Jonathan and Szabo, Richard J. (2008) D-branes, RR-fields and duality on noncommutative manifolds. Communications in Mathematical Physics, 277 (3), 643-706. (doi:10.1007/s00220-007-0396-y).

Record type: Article

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 noncom4 mutative 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.

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e-pub ahead of print date: 5 December 2007
Published date: 5 February 2008

Identifiers

Local EPrints ID: 49723
URI: https://eprints.soton.ac.uk/id/eprint/49723
ISSN: 0010-3616
PURE UUID: 32a9471f-7e01-4c40-aae8-6b28d4dc9bf3

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Date deposited: 26 Nov 2007
Last modified: 11 Nov 2019 19:24

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