I have an answer to your point 1) and if you have something about it please, let me know. Yang-Mills theory in D=1+1 is trivial and has no dynamics. This is a fact known since ’70s after ‘t Hooft solved QCD in this case. You know that, even if there is no propagating degree of freedom for Yang-Mills, full QCD in this case is interesting yet. The conformal solution, obtained with a kind of truncation of the Dyson-Schwinger hierarchy, corresponds exactly to this case: No propagating degrees of freedom. People that worked in this way just removed any dynamics from the theory in D=3 and 4 making it identical to the two-dimensional case. Currently, people is missing this elementary point about all this matter. There are other severe criticisms for the conformal solution but let me stop here.

About point 2), this is too technical and a matter for lattice specialists. I cannot help.

About point 3), I should say that Gribov ideas, on which derivations of the conformal solution are based, proved till now to be a blind alley. I am convinced that, here, lattice computations are saying the right thing. The right thing is that we can live happily without considering Gribov copies and horizons both in the infrared and in the ultraviolet.

Cheers,

Marco

]]>yes, it clearly shows how hot the debate about scalling/decoupling solution is getting!

I still have some disturbing points, which lattice data failled to probe:

(1) 2d data (from Maas) used \beta much bigger than the values used in 3d and 4d (by Adelaide and São Carlos groups). So, 2d simulations are nearer to continuum… so, why is it contradictory to 3d and 4d?

(2) There is no consensus about how well-controlled systematics on gauge-fixing, continuum and thermodynamical limits have to be to set a real answer.

(3) If the fundamental-modular-Gribov reagion is really important for confinement, well, it is not yet proved that Canonical-ensemble answers (from lattice) will be even able to probe that (i.e. canonical and micro-canonical ensembles may be inequivalent for V->infinity).

I think there is a puzzling state nowadays on this area, much more rigorous work has to be performed before lattice comunity gets a consensus.

Cheers,

Rafael.

]]>Hi Daniel,

I proved quite recently that quark effects are higher order in a 1/g series, see

http://arxiv.org/abs/0812.0934

But, even if things would not stay that way, to know the exact gluon propagator gives immediately a Nambu-Jona-Lasinio model that describes quite well low-energy phenomenology.

SU(2) or SU(3) does not change anything as has been proved in studies with Dyson-Schwinger equations. It is just more convenient from a computational standpoint.

Cheers,

Marco

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