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}
}
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… 

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References

SHOWING 1-10 OF 41 REFERENCES

A Groupoid Approach to Noncommutative T-Duality

Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows

Topology and H-flux of T-dual manifolds.

A general formula for the topology and H-flux of the T-dual of a type II compactification is presented, finding that the manifolds on each side of the duality are circle bundles whose curvatures are given by the integral of theDual H- flux over the dual circle.

T-Duality: Topology Change from H-Flux

T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E8 and also using S-duality. We present known and new examples

On the Topology of T-Duality

We study a topological version of the T-duality relation between pairs consisting of a principal U(1)-bundle equipped with a degree-three integral cohomology class. We describe the homotopy type of a

Topological T-duality, automorphisms and classifying spaces

Periodic Twisted Cohomology and T-Duality

The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a

THE TOPOLOGY OF T-DUALITY FOR Tn-BUNDLES

In string theory, the concept of T-duality between two principal Tn-bundles E and E over the same base space B, together with cohomology classes h ∈ H3(E,ℤ) and ĥ ∈ H3(E,ℤ), has been introduced. One

Duality for topological abelian group stacks and T-duality

We extend Pontrjagin duality from topological abelian groups to certain locally compact group stacks. To this end we develop a sheaf theory on the big site of topological spaces S in order to prove

T-duality for principal torus bundles and dimensionally reduced Gysin sequences

We reexamine the results on the global properties of T-duality for principal circle bundles in the context of a dimensionally reduced Gysin sequence. We will then construct a Gysin sequence for

Sheaf theory for stacks in manifolds and twisted cohomology for S 1 -gerbes

In this paper we give a sheaf theory interpretation of the twisted cohomology of manifolds. To this end we develop a sheaf theory on smooth stacks. The derived push-forward of the constant sheaf with