T-duality for torus bundles with H-fluxes via noncommutative topology
Date
2005
Authors
Varghese, M.
Rosenberg, J.
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Journal article
Citation
Communications in Mathematical Physics, 2005; 253(3):705-721
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Varghese Mathai and Jonathan Rosenberg
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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.
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The original publication is available at www.springerlink.com