Dual formulations of non-Abelian spin models: Local representation and low-temperature asymptotics

Non-Abelian lattice SU(N) or U(N) spin models 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 and some observables of such models on a cubic lattice in arbitrary dimension D. An interaction between dual variables ranges over one given hypercube of the dual lattice. We use our construction to study the dual of SU(2) model in two dimensions. Leading terms of the asymptotic expansion of the dual weight are computed and it is proven that at low temperatures it converges to a certain Gaussian distribution uniformly in fluctuations of dual variables. This result enables us to define the semiclassical limit of the dual formulation and to extract leading perturbative contribution to the correlation function which shows power-like decay. We present some analytical evidences that the low-temperature limit of the dual formulation is described by ISO(2)-like approximation of SU(2) matrices