Topological T-duality and T-folds

Abstract

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 ${\mathcal A} \rtimes_{α|_{\KZ^d}} {\mathbb Z}^d$ 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.

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

References in corpus (2)

• On the Topology and Flux of T-Dual Manifolds
• T-duality, Gerbes and Loop Spaces