Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions

Abstract

We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit. Our proposal contains a single parameter with dimensions of mass; confinement via dimensional reduction is obtained if this parameter is non-zero, and a non-zero value appears to be energetically preferred. A method for numerical simulation of this vacuum state is developed. It is shown that if the mass parameter is fixed from the known string tension in 2+1 dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.

14 pages, 9 figures. v2: Typos corrected. v3: added a new section discussing alternative (new variables) approaches, and fixed a problem with the appearance of figures in the pdf version. Version to appear in Phys Rev D

References in corpus (13)

• Coulomb Gauge QCD, Confinement, and the Constituent Representation
• On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions
• On the Yang-Mills wave functional in Coulomb gauge
• Color Screening, Casimir Scaling, and Domain Structure in G(2) and SU(N) Gauge Theories
• A variational approach to the QCD wave functional:Dynamical mass generation and confinement
• A precise calculation of the fundamental string tension in SU(N) gauge theories in 2+1 dimensions
• Glueball Regge Trajectories in (2+1) Dimensional Gauge Theories
• On the Glueball Spectrum of Pure Yang-Mills Theory in 2+1 Dimensions
• Continuum Strong Coupling Expansion of Yang-Mills Theory: Quark Confinement and Infra-Red Slavery
• On the $0^{++}$ Glueball Mass
• Yang-Mills Theory in 2+1 Dimensions: Coupling of Matter Fields and String-breaking Effects
• Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled Yang-Mills Theory
• A conjecture on the infrared structure of the vacuum Schrodinger wave functional of QCD

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