  We study a connection between duality and topological field theories. First,
2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more
or less Poincare duality), and a similar formulation is given for
higher-dimensional cases. In this form they lead to simple TFTs with boundary
coloured in two colours. The statistical models live on the boundary of these
TFTs, as in the CS/WZW or AdS/CFT correspondence. Classical models (Poisson-Lie
T-duality) suggest a non-abelian generalization in the 2dcase, with abelian
groups replaced by quantum groups. Amazingly, the TFT formulation solves the
problem without computation: quantum groups appear in pictures, independently
of the classical motivation. Connection with Chern-Simons theory appears at the
symplectic level, and also in the pictures of the Drinfeld double:
Reshetikhin-Turaev invariants of links in 3-manifolds, computed from the
double, are included in these TFTs. All this suggests nice phenomena in higher
dimensions.
