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Type: Journal article
Title: T-duality for torus bundles with H-fluxes via noncommutative topology
Author: Varghese, M.
Rosenberg, J.
Citation: Communications in Mathematical Physics, 2005; 253(3):705-721
Publisher: Springer
Issue Date: 2005
ISSN: 0010-3616
Statement of
Varghese Mathai and Jonathan Rosenberg
Abstract: It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a torus bundle. A big puzzle has been to explain these mysterious missing T-duals. Here we show that this problem is resolved using noncommutative topology. It turns out that every principal T2-bundle with H-flux does indeed have a T-dual, but in the missing cases (which we characterize), the T-dual is non-classical and is a bundle of noncommutative tori. The duality comes with an isomorphism of twisted K-theories, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced by an isomorphism of twisted cyclic homology.
Description: The original publication is available at
DOI: 10.1007/s00220-004-1159-7
Published version:
Appears in Collections:Aurora harvest 2
Pure Mathematics publications

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