Bunke, Ulrich and Nikolaus, Thomas (2015) T-duality via gerby geometry and reductions. REVIEWS IN MATHEMATICAL PHYSICS, 27 (5): 1550013. ISSN 0129-055X, 1793-6659
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We consider topological T-duality of torus bundles equipped with (S) under bar (1)-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S-1-valued functions which are constant along the torus fibers. We observe that such a reduction is exactly the additional datum needed for the construction of a T-dual pair. We illustrate the theory by working out the example of the canonical lifting gerbe on a compact Lie group which is a torus bundle over the associated flag manifold. It was a recent observation of Daenzer and van Erp [16] that for certain compact Lie groups and a particular choice of the gerbe, the T-dual torus bundle is given by the Langlands dual group.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | BUNDLE GERBES; TORUS BUNDLES; NONCOMMUTATIVE TOPOLOGY; H-FLUXES; COHOMOLOGY; T-duality; gerbes; Langlands dual group; stacks |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Petra Gürster |
| Date Deposited: | 21 Aug 2020 06:41 |
| Last Modified: | 21 Aug 2020 06:41 |
| URI: | https://pred.uni-regensburg.de/id/eprint/5394 |
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