Reading arxiv dailys today I have found three different papers on the gluon and ghost propagators for Yang-Mills (see here, here and here). These papers prove that this line of research is very strongly alive and that there exist a lot of points to be settled down before to carry on. In this post I would like to point out several evidences that should not be forgotten when one talks about this matter. First of all there are the results of Yang-Mills theory in D=1+1. We know that, for this dimensionality, Yang-Mills theory has no dynamics. Anyhow, several people tried to solve it on the lattice or modified it to try to relate these solutions of the ones of Dyson-Schwinger equations with a given truncation. The bad news is that they find agreement with such solutions of Dyson-Schwinger equations. Why is this bad news? Because this gives, beyond any doubt, a proof that such a truncation of Dyson-Schwinger equations is fault as it removes any dynamics from Yang-Mills theory in higher dimensionality and appears to agree with numerical results just when such a dynamics does not exist. This is already a severe indicator that lattice computations done in higher dimensionality are right. What do they say us about ghost and gluon propagators?
- Gluon propagator reaches a non-null finite value at zero momenta.
- Ghost propagator is that of a free particle.
- Running coupling goes to zero at lower momenta.
This means that the confinement scenarios that are normally considered are faulty and do not work at all. These results demand for a better understanding of the physical situation at hand. It we are not ourselves convinced that they are right, we will keep on fumbling in the dark losing precious resources and time. Evidences are really heavy already at this stage and should be combined with spectra computations carried out so far. Also in this case a lot of work still must be carried out. You can read the beatiful paper of Craig McNeile about (contribution to QCD 08). It is a mistery to me why these ways are seen as different into the understanding of Yang-Mills theory.