T-duality for torus bundles with H-fluxes via noncommutative topology, II: the high-dimensional case and the T-duality group
Date
2006
Authors
Varghese, M.
Rosenberg, J.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Advances in Theoretical and Mathematical Physics, 2006; 10(1):123-158
Statement of Responsibility
Varghese Mathai and Jonathan Rosenberg
Conference Name
Abstract
We use noncommutative topology to study T-duality for principal torus bundles with H-flux. We characterize precisely when there is a "classical" T-dual, i.e., a dual bundle with dual H-flux, and when the T-dual must be "nonclassical," that is, a continuous field of noncommutative tori. The duality comes with an isomorphism of twisted K-theories, required for matching of D-brane charges, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced in the nonclassical case by an isomorphism of twisted cyclic homology. An important part of the paper contains a detailed analysis of the classifying space for topological T-duality, as well as the T-duality group and its action. The issue of possible nonuniqueness of T-duals can be studied via the action of the T-duality group. © 2006 International Press.