The topology of T-duality for T^n-bundles

Details The topology of T-duality for T^n-bundles The topology of T-duality for T^n-bundles

2005-01-27

arxiv.org/abs/math/0501487v5

Reviews in Mathematical Physics, Vol. 18, No. 10 (2006) 1103-1154

Mathematics

Geometric Topology

67 pages, LaTex2e. The revised version contains in particular an extended introduction explaining the physical background. Fin

Scientific paper

10.1142/S0129055X06002875

In string theory, the concept of T-duality between two principal T^n-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. We construct a classifying space for pairs as above with additional "dualizing data", with a forgetful map to the classifying space for pairs (also constructed in the paper). On the first classifying space, we have an involution which corresponds to passage to the dual pair, i.e. to each pair with dualizing data exists a well defined dual pair (with dualizing data). We show that a pair (E,h) can be lifted to a pair with dualizing data if an only if h belongs to the second step of the Leray-Serre filtration of E (i.e. not always), and that in general many different lifts exist, with topologically different dual bundles. We establish several properties of the T-dual pairs. In particular, we prove a T-duality isomorphism of degree -n for twisted K-theory.

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