Integrable Models and Confinement in (2 + 1)-dimensional Weakly-coupled Yang-mills Theory

We generalize the (2 + 1)-dimensional Yang-Mills theory to an anisotropic form with two gauge coupling constants e and e. In axial gauge, a regularized version of the Hamiltonian of this gauge theory is H0 + e H1, where H0 is the Hamiltonian of a set of (1 + 1)-dimensional principal chiral sigma nonlinear models and H1 couples charge densities of these sigma models. We treatH1 as the interaction Hamiltonian. For gauge group SU(2), we use form factors of the currents of the principal chiral sigma models to compute the string tension for small e, after reviewing exact S-matrix and formfactor methods. In the anisotropic regime, the dependence of the string tension on the coupling constants is not in accord with generally-accepted dimensional arguments. [email protected]