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2008

Topological T-duality and T-folds

Bouwknegt, Peter, Pande, Ashwin S.

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We explicitly construct the C*-algebras arising in the formalism of Topological T-duality due to Mathai and Rosenberg from string-theoretic data in several key examples.

We construct a continuous-trace algebra with an action of ${\mathbb R}^d$ unique up to exterior equivalence from the data of a smooth ${\mathbb T}^d$-equivariant gerbe on a trivial bundle $X = W \times {\mathbb T}^d$.
We argue that the `noncommutative T-duals' of Mathai and Rosenberg, should be identified with the nongeometric backgrounds well-known in string theory.
We also argue that the crossed-product C*-algebra ${\mathcal A} \rtimes_{\alpha|_{\KZ^d}} {\mathbb Z}^d$ should be identified with the T-folds of Hull which geometrize these backgrounds.

Topological T-duality and T-folds · Around

Built on

I. Raeburn and J. Rosenberg, Crossed products of continuous-trace C ∗ C^{\ast} -algebras by smooth actions
1988
Earlier work this paper cites.
P. Baier, Thesis, University of Oxford, Special Lagrangian Geometry
2001
Earlier work this paper cites.
S. Hellerman, J. McGreevy and B. Williams, Geometric Construction of Nongeometric String Theories
2004
Earlier work this paper cites.
P. Bouwknegt, J. Evslin and V. Mathai, On the Topology and H-flux of T-dual Manifolds
2004
Earlier work this paper cites.

Similar

C.M. Hull, A Geometry for Non-Geometric String Backgrounds
2005
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V. Mathai and J. Rosenberg, T-Duality for Torus Bundles with H-fluxes via Noncommutative Topology
2005
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P. Bouwknegt, K. Hannabuss and V. Mathai, T-duality for principal torus bundles and dimensionally reduced Gysin sequences
2005
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V. Mathai and J. Rosenberg, T-Duality for Torus Bundles with H-fluxes via Noncommutative Topology II
2006
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D.M. Belov, C.M. Hull and R. Minasian, T-duality, Gerbes and Loop Spaces
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D. Vegh and J. McGreevy, Semi-Flatland
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S. Echterhoff, R. Nest and H. Oyono-Oyono, Principal Noncommutative torus bundles
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S. Echterhoff, R. Nest and H. Oyono-Oyono, Fibrations with noncommutative fibers
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Then

A. Lawrence, M.B. Schulz and B. Wecht, D-Branes in Nongeometric Backgrounds
2006
Later among the works it cites.
R.M.G. Reis and R.J. Szabo, Geometric K-Homology of Flat D-Branes
2006
Later among the works it cites.
P. Grange and S. Schäfer-Nameki, T-duality with H H -flux: non-commutativity, T-folds and G × G G\times G -structures
2007
Later among the works it cites.

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