ABSTRACT

Let $X$ be the topological space associated to a finite-dimensional manifold and suppose $p:X \to W$ is a principal circle bundle.

We consider $C_0(X)$-algebras $\D$ which are section algebras of locally trivial $C^{\ast}$-bundles over $X$ with fiber $\A \otimes \Cpct$ where $\A$ is a strongly self-absorbing $C^{\ast}$-algebra. We discuss in detail how to generalize Topological T-duality of Mathai and Rosenberg to these algebras. We argue that  we may use the $S^1-$action on $X$ together with some extra data to define a Topological T-dual $C^{\ast}-$algebra. We also calculate some examples of this Topological T-dual. We outline a set of proposed physical applications of this formalism to String Theory.

Keywords: Topologica T-duality, Strongly Self-Absorbing $C^{\ast}-$algebras, String Theory and T-duality, Fermionic T-duality, Timelike T-duality, AdS/CFT Duality