• DOI:10.1142/S0129055X15500130
• Corpus ID: 73635793

T-Duality via Gerby Geometry and Reductions

@article{Bunke2013TDualityVG,
  title={T-Duality via Gerby Geometry and Reductions},
  author={Ulrich Bunke and Thomas Nickelsen Nikolaus},
  journal={arXiv: Differential Geometry},
  year={2013}
}

• U. Bunke, T. Nikolaus
• Published 26 May 2013
• Mathematics
• arXiv: Differential Geometry

We consider topological T-duality of torus bundles equipped with S^{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 fibres. 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 bundles over the associated flag manifold. It was a recent observation of Daenzer and van Erp (arXiv1211.0763) 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.