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

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

2006-07-03

arxiv.org/abs/hep-th/0607013v6

Phys.Rev.D74:085001,2006

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.74.085001

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.

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