What's up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices

Question

Referee this paper: arXiv:0710.0412v1 by Attilio Cucchieri, Tereza Mendes

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

(Is this your paper?)

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Comments

This paper is working in a crazy gauge to produce long-distance correlations where there are none. These are obviously an artifact of Landau gauge, they are purely gauge correlations, not physical correlations, as can be proved assuming mass-gap. I am writing this comment to quickly explain what is going on here, while preparing a full review. A full review needs to describe what is going on in the guts of Landau gauge stuff, which is hard, because it is a very difficult gauge numerically. It is possible that this paper is correctly disproving the Gribov-Zwanziger Landau-gauge propagator scenario, but it is not disproving mass-gap, nor is it disproving the Wilsonian picture of long-range uncorrelated gauge fields described by strong coupling expansion. Any long-range correlations in the gauge field does not appear in gauge-unfixed simulations (which is what everyone normally does, as you don't need to fix a gauge on the lattice), and are a property of Landau gauge. To see this, the easiest way is to use a different gauge.

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Ron, this paper is just showing that there is a mass gap. It is strange how you did not realize this. The best fit is with a propagator like

\(G(p)=\frac{A_1}{p^2+m_1^2}+\frac{A_2}{p^2+m_2^2}+\ldots\)

and is the Gribov-Zwanzinger scenario that does not fit the bill. Please, avoid your review in order to not become a fool of yourself and keep this site on the serious side.

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Of course, currently I am the only one aware of this story and able to comment but I will do this if Ron will be stopped from doing such a foolish thing.

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No, this paper is not "just showing that there is a mass gap", it is claiming to show that the Gribov-Zwanziger ansatz for the Landau-gauge propagator is wrong, and that the gauge-gauge correlator in Landau gauge has a residual correlation at q=0 that is not there in the traditional ansatz.

This claim might be correct, it might not be correct. I did not write a review because I don't know if it is correct or not, it requires a lot of thinking, and a close analysis of the numerical method of going to Landau gauge, which is tricky numerically.

On the other hand, you have been misusing this paper to argue that Wilson's strong coupling expansion picture is naive or misguided. To remind folks: the strong coupling picture shows that the gauge-unfixed gauge theory has completely uncorrelated long-range gauge-fields, each distant region in the gauge theory is completely statistically independent of any other region. By "distant", I mean larger than the confinement length (or the inverse mass gap), and the complete independence is equivalent in strong-coupling expansion to the statement of mass gap in the theory, as the mass gap is the rate of exponential decay of all gauge-invariant correlators.

You imply that this fundamental ancient result is somehow modified, somehow made incorrect, or somehow overthrown by current simulations. It cannot be overthrown, as the convergence of lattice fields at long distances to the predictions of the strong coupling expansion has been verified over many decades of gauge unfixed simulations, and it is easy to reproduce this particular calculation on any PC for yourself (unlike the lattice simulations in this paper).

I agree that you can make some good mass gap heuristic fits to the Landau-gauge propagator: the constant behavior of the propagator at q=0 in massive free field theory (as opposed to rising behavior in ungapped theories) is the local correlation contribution for a field which is clamped to a fixed point at long distances, and this seems like it is what is going on in the Landau gauge thing, local correlations only. But these are somehow clamped to some fixed value long-range thing, like the value $\phi=0$ in massive free scalar field theory is a global value the field fluctuation mean is clamped to.

The issue here is something else--- that the gribov-Zwanziger scenario is supposed to model the fact that all gauge-field correlations at long-distance vanish, as all correlations do in gauge unfixed simulation. and this paper while attacking this scenario can be interpreted as claiming that distant  regions in gauge theory can be correlated on the lattice. This claim is incorrect in the normal no-gauge-fixing lattice gauge.

This property of long-range clamping or somehow statistical non-independence is simply an artifact of Landau gauge. There are no correlations at all at long distances when you don't gauge fix the lattice action.

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Again an uninformed intervention by you. This people performed these computations in a full range of gauges. Please, avoid this lengthy and wrong comments claiming incompetent all others rather than you. You are fully out of date in this area of research that involved a lot of well trained people for about twenty years.