Infrared Gluon and Ghost Propagators

We derive the form of the infrared gluon propagator by proving a mapping in the infrared of the quantum Yang-Mills and $\lambda\phi^4$ theories. The equivalence is complete at a classical level. But while at a quantum level, the correspondence is spoiled by quantum fluctuations in the ultraviolet limit, we prove that it holds in the infrared where the coupling constant happens to be very large. The infrared propagator is then obtained from the quantum field theory of the scalar field producing a full spectrum. The results are in fully agreement with recent lattice computations. We get a finite propagator at zero momentum, the ghost propagator going to infinity as $1/p^{2+2\kappa}$ with $\kappa=0$.Comment: 7 pages, no figure. After proofs correction. To appear in Physics Letters

Confinement in a three-dimensional Yang-Mills theory

We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.Comment: 12 pages, no figure. Version accepted for publication in European Physical Journal C. arXiv admin note: substantial text overlap with arXiv:1408.465