Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled Yang-Mills Theory

Abstract

We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form with two gauge coupling constants $e$ and $e^{\prime }$. In an axial gauge, a regularized version of the Hamiltonian of this gauge theory is $H_0+{e^{\prime }}^2{H}_1$, where $H_0$ is the Hamiltonian of a set of (1+1)-dimensional principal chiral nonlinear sigma models. We treat $H_1$ 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 $e^{\prime }$, after reviewing exact S-matrix and form-factor methods. In the anisotropic regime, the dependence of the string tension on the coupling constant is not in accord with generally-accepted dimensional arguments.

Now 37 pages, Section 5 moved to an appendix, more motivation given in the introduction, a few more typos corrected

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