Topological T-duality and T-folds

Details Topological T-duality and T-folds Topological T-duality and T-folds

2008-10-24

arxiv.org/abs/0810.4374v2

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, no figures, uses xypic, minor typos corrected

Scientific paper

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. We identify the charge group of D-branes on T-fold backgrounds in the C*-algebraic formalism of Topological T-duality. We also study D-branes on T-fold backgrounds. We show that the $K$-theory bundles studied by Echterhoff, Nest and Oyono-Oyono give a natural description of these objects.

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