We generalize the $(2+1)$-dimensional Yang-Mills theory to an anisotropic form with two gauge coupling constants $e$ and $e^{\prime }$. In 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 sigma nonlinear models and $H_1$ couples charge densities of these 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 constants is not in accord with generally-accepted dimensional arguments.

• Received 4 July 2006

DOI:https://doi.org/10.1103/PhysRevD.74.085001