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

References in corpus (15)

• (De)Constructing Dimensions
• SU(N) gauge theories in 2+1 dimensions
• Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models
• Exact Form Factors in Integrable Quantum Field Theories: the Sine-Gordon Model
• On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions
• A gauge-invariant Hamiltonian analysis for non-Abelian gauge theories in (2+1) dimensions
• Exact form factors in integrable quantum field theories: the sine-Gordon model (II)
• On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions
• Principal Chiral Field at Large N
• Gauge invariant variables and the Yang-Mills-Chern-Simons theory
• Manifest covariance and the Hamiltonian approach to mass gap in (2+1)-dimensional Yang-Mills theory
• A new set of exact form factors
• Lattice QCD-2+1
• Gauge-Invariant Coordinates on Gauge-Theory Orbit Space
• Extremal Curves in 2+1-Dimensional Yang-Mills Theory

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