Kramers-Wannier duality is a symmetry relating the high-and low-temperature phases of
the 2-dimensional lattice Ising model. Electric-Magnetic duality is a 3-dimensional
duality between abelian (flat) gauge theories for Pontryagin dual abelian groups. Both
dualities generalize to higher-dimensional manifolds. We describe the relation between
them using the notion of relative field theory. The order and disorder operators of the
Ising model are endpoints of Wilson and t’Hooft electro-magnetic loops, respectively.
There is a higher-dimensional generalization to finite homotopy types.
This is based on joint work with Dan Freed.