  We present an exact duality transformation in the framework of Statistical
Mechanics for various lattice models with non-Abelian global or local
symmetries. The transformation applies to sigma models with variables in a
compact Lie group G with global GxG-symmetry (the chiral model) and with
variables in coset spaces G/H and a global G-symmetry (for example, the
non-linear O(N) or RP^N models) in any dimension d>=1. It is also available for
lattice gauge theories with local gauge symmetry in dimensions d>=2 and for the
models obtained from minimally coupling a sigma model of the type mentioned
above to a gauge theory. The duality transformation maps the strong coupling
regime of the original model to the weak coupling regime of the dual model.
Transformations are available for the partition function, for expectation
values of fundamental variables (correlators and generalized Wilson loops) and
for expectation values in the dual model which correspond in the original
formulation to certain ratios of partition functions (free energies of
dislocations, vortices or monopoles). Whereas the original models are
formulated in terms of compact Lie groups G and H, coset spaces G/H and
integrals over them, the configurations of the dual model are given in terms of
representations and intertwiners of G. They are spin networks and spin foams.
The partition function of the dual model describes the group theoretic aspects
of the strong coupling expansion in a closed form.
