## SU(2) lattice gauge theory revisited

As my readers know, there are several groups around the World doing groundbreaking work in lattice gauge theories. I would like here to cite names of I. L. BogolubskyE.-M. IlgenfritzM. Müller-Preussker, and  A. Sternbeck jointly working in Russia, Germany and Australia. They have already produced a lot of meaningful papers in this area and today come out with another one worthwhile to be cited (see here). I would like to cite a couple of their results here. Firstly, they show again that the decoupling type solution in the infrared is supported. They get the following figure

The gauge is the Landau gauge. They keep the physical volume constant at 10 fm while varying the linear dimension and the coupling. This picture is really beautiful confirming an emergent understanding of the behavior of Yang-Mills theory in the infrared that we have supported since we opened up this blog. But, I think that a second important conclusion from these authors is that Gribov copies do not seem to matter. Gribov ambiguity has been a fundamental idea in building our understanding of gauge theories and now it just seems it has been a blind alley for a lot of researchers.

All this scenario is fully consistent with our works on pure Yang-Mills theory. As far as I can tell, there is no theoretical attempt to solve these equations than ours being in such agreement with lattice data (running coupling included).

I would finally point out to your attention a very good experimental paper from KLOE collaboration. This is a detector at ${\rm DA\Phi NE}$  accelerator in Frascati (Rome). They are carrying out a lot of very good work. This time they give the decay constant of the pion on energy ranging from 0.1 to 0.85 ${\rm GeV^2}$ (see here).

### 2 Responses to SU(2) lattice gauge theory revisited

1. Rafael Frigori says:

Dear Marco, how are you doing?

I have just completed a work that may be of your interest:
http://xxx.lanl.gov/abs/0912.2871
Regards,

Rafael

• mfrasca says:

Dear Rafael,

I am fine. Thank you very much for your beautiful paper. It is a great news! Please, note that my paper with the answer to Terry Tao 0903.2357 has gone published in Modern Physics Letters A. You can find the exact reference in the above link. You can also read an exchange with Terry here. I was not able to convince him to plead for me but, as you can read, he consider my last proof correct.

Your lattice computations are soundly confirming my findings and in a really striking and unexpected way. Mapping indeed exists and now it is not just a mathematical proof but you have seen it by numerically solving quantum field theory! It is interesting to note that the first authors to point out that Yang-Mills theory in d=2+1 has a tower of excitations were McKellar and Carlsson here and here. Since then, there have been several good works about all confirming this idea even if not explicitly as zeros of Bessel functions that, indeed, in some limit recover the harmonic oscillator spectrum.

Please, take my best greetings to Attilio e Tereza. They must keep up with their excellent work as longer as possible.

Thank you very much again. I will take some time to write about this in a post.

Best,

Marco

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