  Non-abelian lattice spin models with symmetry group SU(N) or U(N) can be
formulated in terms of link variables which are subject to the Bianchi
constraints. Using this representation we derive exact and local dual
formulation for the partition function of such models on a cubic lattice in
arbitrary dimension D. Locality means that the dual action is given by a sum
over some subset of hypercubes of the dual lattice and the interaction between
dual variables ranges over one given hypercube. Dual variables are in general
discrete-valued and live on (D-2)-cell of the dual lattice, in close analogy
with the XY model. We use our construction to study in details the dual of
SU(2) principal chiral model in two dimensions. We give dual expressions also
for two-point correlation function in arbitrary representation and for the free
energy of defects. Leading terms of the asymptotic expansion of the dual
Boltzmann factor are computed and it is proven that at low temperatures it
converges to a certain Gaussian distribution uniformly in all fluctuations of
dual variables. This result enables us to define the semiclassical limit of the
dual formulation and to determine an analog of the vortex--spin-wave
representation for the partition function. Such representation is used to
extract leading perturbative contribution to the correlation function which
shows power-like decay at weak coupling. We also present some analytical
evidences that the low-temperature limit of the dual formulation is completely
described by ISO(2)-like approximation of SU(2) matrix elements.
