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

TL;DR

This paper explores a generalized (2+1)-dimensional Yang-Mills theory with anisotropic couplings, analyzing its Hamiltonian structure and calculating string tensions using form factors, revealing unexpected dependence on coupling constants.

Contribution

It introduces an anisotropic extension of (2+1)D Yang-Mills theory and applies form-factor techniques to compute string tensions, providing new insights into confinement mechanisms.

Findings

String tension computed for small e' using form factors.

Dependence of string tension on coupling constants differs from traditional dimensional analysis.

Hamiltonian structure relates to (1+1)D principal chiral models.

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.