Bunke, U. and Schick, T.: On the topology of T-duality
Abstract:
In string theory, the concept of T-duality between two principal
$U(1)$-bundles $E_1$ and $E_2$ over the same base space $B$, together with
cohomology classes $h_1\in H^3(E_1)$ and $h_2\in H^3(E_2)$, has been
introduced. One of the main virtues of T-duality is that
$h_1$-twisted K-theory of $E_1$ is isomorphic to $h_2$-twisted
K-theory of $E_2$.
In this paper, a new, very topological concept of T-duality is
introduced. The study pairs $(E,h)$ as above from a topological
point of view and construct a classifying space of such pairs. Using
this, we construct a universal dual pair to a given pair. Our
construction immediately gives a number of known and new properties
of the dual. In particular it implies existence of a dual of any
pair $(E,h)$, and it
also describes the ambiguity upto which the dual is well defined.
In order to deal with twisted K-theory, some care is needed, in
particular when dealing with naturality questions, because the
twisted K-theory depends on the explicit model for the twists and
the twisted theory ---care which is missing in some of the existing
literature. We illustrate the use of T-duality by some explicit
calculations of twisted K-groups.
Thomas Schick