Back at home, conference ended. A lot of good impressions both from the physics side and other aspects as the city and the company. On Friday I held my talk. All went fine and I was goodly inspired so to express my ideas at best. You can find all the talks here. The pictures are here. Now it should be easier to identify me.

**Disclaimer**: The talks I will comment on are about results very near my research area. Talks I will not cite are important and interesting as well and the fact that I will not comment about them does not imply merit for good or bad. Anyhow, I will appreciate any comment by any participant to the conference aiming to discuss his/her work.

On Tuesday afternoon started a session about phases in QCD. This field is very active and is a field where some breakthroughs are expected to be seen in the near future. I have had a lot of fun to know Eduardo Fraga that was here with two of his students: Leticia Palhares and Ana Mizher. I invite you to read their talks as this people are doing a real fine work. On the same afternoon I listened to the talk of Pedro Bicudo. Pedro, besides being a nice company for fun, is also a very good physicist performing relevant work in the area of lattice QCD. He is a pioneer in the use of CUDA, parallel computing using graphic processors, and I intend to use his code, produced with his student Nuno Cardoso, on my machine to start doing lattice QCD at very low cost. On his talk you can see a photo of one of my graphic cards. He used lattice computations to understand the phase diagram of QCD. Quite interesting has been the talk of Jan Pawlowski about the phase diagram of two flavor QCD. He belongs to a group of people that produced the so called scaling solution and it is a great moment to see them to recognize the very existence of the decoupling solution, the only one presently seen on lattice computations.

On Wednesday the morning session continued on the same line of the preceding day. I would like to cite the work of Marco Ruggieri because, besides being a fine drinking companion (see below), he faces an interesting problem: How does the ground state of QCD change in presence of a strong magnetic field? Particularly interesting is to see how the phase diagram gets modified. On the same line were the successive talks of Ana Mizher and Maxim Chernodub. Chernodub presented a claim that in this case vacuum is that of an electromagnetic superconductor due to meson condensation. In this area of research the main approach is to use some phenomenological model. Ana Mizher used a linear sigma model while Marco preferred the Nambu-Jona-Lasinio model. The reason for this is that the low-energy behavior of QCD is not under control and the use of well-supported effective models is the smarter approach we have at our disposal. Of course, this explains why the work of our community is so important: If we are able to model the propagator of the gluon in the infrared, all the parameters of the Nambu-Jona-Lasinio model are properly fixed and we have the true infrared limit of QCD. So, the stake is very high here.

In the afternoon there were some talks that touched very near the question of infrared propagators. Silvio Sorella is an Italian theoretical physicist living in Brazil. He is doing a very good work in this quest for an understanding of the low-energy behavior of QCD. This work is done in collaboration with several other physicists. The idea is to modify the Gribov-Zwanziger scenario, that by itself will produce the scaling solution currently not seen on the lattice, to include the presence of a gluon condensate. This has the effect to produce massive propagators that agree well with lattice computations. In this talk Silvio showed how this approach can give the masses of the lowest states of the glueball spectrum. This has been an important step forward showing how this approach can be used to give experimental forecasts. Daniel Zwanziger then presented a view of the confinement scenario. The conclusion was very frustrating: So far nobody can go to the Clay Institute to claim the prize. More time is needed. Daniel has been the one who proposed the scenario of infrared Yang-Mills theory that produced the scaling solution. The idea is to take into account the problem of Gribov copies and to impose that all the computations must be limited to the first Gribov horizon. If you do this the gluon propagator goes to zero lowering momenta and you get positivity maximally violated obtaining a confining theory. So, this scenario has been called Gribov-Zwanzinger. From lattice computations we learned that the gluon propagator reaches a non zero finite value lowering momenta and this motivated Silvio and others to see if one could maintain the original idea of Gribov horizon and agreement with lattice computations of the Gribov-Zwanzinger scenario. Matthieu Thissier presented a talk with an original view. The idea is to consider QCD with a small perturbation expansion at one loop and a mass term added by hand. He computed the gluon propagator and compared with lattice data till the infrared obtaining a very good agreement. Arlene Aguilar criticized strongly this approach as he worked with a coupling larger than one (a huge one said Arlene) even if he was doing small perturbation theory. I talked about this with Matthieu. My view is that the main thing to learn from this kind of computations is that if you take a Yukawa-like propagator with a mass going at least as (do you remember Orlando Oliveira talk?) the agreement with lattice data is surely fairly good and so, even if you have done something that is mathematically questionable, surely we apprehend an important fact! The afternoon session was concluded by the talk of Daniele Binosi. With Daniele we spent a nice night in Ghent. He is a student of Joannis Papavassiliou and, together with Arlene Aguilar, this group is doing fine work on numerically solving Dyson-Schwinger equations to get the full propagator of Yang-Mills theory. They get a very good agreement with lattice data and support the view that, on the full range of energies, the Cornwall propagator for the gluon with a logarithmic running mass reaching a constant in the infrared is the right description of the theory. Daniele presented a beautiful computation based on Batalin-Vilkoviski framework that supported the conclusions of his group. It should be said that he presented a different definition of the running coupling that grants a non-trivial fixed point at infrared. This is a delicate matter as, already a proper definition of the running coupling for the infrared is not a trivial question. Daniele’s definition is quite different from that given by Andre Sternbeck in his talk as the latter has just the trivial fixed point as is emerging from the lattice computations.

On Thursday the first speaker was Attilio Cucchieri. Attilio and his wife, Tereza Mendes, are doing a fine work on lattice computations that reached a breakthrough at Lattice 2007 when they showed, with a volume of , that the gluon propagator in the Landau gauge reaches a finite non-zero value lowering momenta. This was a breakthrough, confirmed at the same conference by two others groups (Orlando Oliveira by one side and I. Bogolubsky, E.M. Ilgenfritz, M. Muller-Preussker and A. Sternbeck by the other side), as for long time it was believed that the only true solution was the scaling one and the gluon propagator should have gone to zero lowering momenta. This became a paradigm so that papers have got rejected on the basis that they were claiming a different scenario. Attilio this time was on a very conservative side presenting an interesting technical problem. Tereza’s talk was more impressive showing that, with higher temperatures and increasing volumes, in the Landau gauge the plateau is still there. With Tereza and Attilio we spent some nice time in a pub discussing together with Marco Ruggeri about the history of their community, how they went to change everything about this matter and their fighting for this. I hope one day this people will write down this history because there is a lot to learn from it. In the afternoon session there was a talk by Reinhard Alkofer. Alkofer has been instrumental in transforming the scaling solution into a paradigm for a lot of years in the community. Unfortunately lattice computations talked against it and, as Bob Dylan one time said, times are changing. He helped the community with discovering a lot of smart students that have given an important contribution to it. In his talk he insisted with his view with a proposal for the functional form for the propagator (this was missing until now for the scaling solution) and a computation of the mass of the . is a very strange particle. From (KLOE-2) we know that this is not just a composite state of quarks but it contains a large part made of glue: It is like to have to cope with an excited hydrogen atom and so, also its decay is to be understood (you can read my paper here). So, maybe a more involved discussion is needed before to have an idea of how to get the mass of this particle. After Alkofer’s talk followed the talks of Aguilar and Papavassiliou. I would like to emphasize the relevance of the work of this group. Aguilar showed how they get an effective quark mass from Schwinger-Dyson equations when there is no enhancement in the ghost propagator. Papavassiliou proposed to extend the background field method to Schwinger-Dyson equations. I invite you to check the agreement they get for the Cornwall propagator of the gluon with lattice data in Arlene’s talk and how this can give the form at lower momenta. My view is that, combining my recent results on strongly coupled expansions for Yang-Mills and scalar field theories and the results of this group, a meaningful scenario is emerging giving a complete comprehension of what is going on for Yang-Mills theory at lower energies. Joannis gave us an appointment for the next year in Trento. I will do everything I can to be there! Finally, the session was completed with Axel Mass’ talk. Axel has been a student of Alkofer and worked with Attilio and Tereza. He put forward a lattice computation of Yang-Mills propagators in two dimensions that, for me, should have completely settled the question but produced a lot of debate instead. He gave in his talk another bright idea: To study on the lattice a scalar theory interacting with gluons. I think that this is a very smart way to understand the mechanism underlying mass generation in these theories. From the works discussed so far it should appear clear that Schwinger mechanism (also at classical level (see my talk)!) is at work here. The talk of Axel manifestly shows this. It would be interesting if he could redo the computations taking a massless scalar field to unveil completely the dynamical generation of masses.

On Friday the morning session started with an interesting talk by Hans Dierckx trying to understand cardiac behavior using string theory. A talk by Oliver Rosten followed. Oliver produced a PhD thesis on the exact renormalization group of about 500 pages (see here). His talk was very beautiful and informative and in some way gave a support to mine. Indeed, he showed, discussing on the renormalization group, how a strong coupling expansion could emerge. In some way we are complimentary. I will not discuss my talk here but you are free to ask questions. The conference was concluded by a talk of Peter van Baal. Peter has a terrible story about him and I will not discuss it here. I can only wish to him the best of the possible lucks.

Finally, I would like to thank the organizers for the beautiful conference they gave me the chance to join. The place was very nice (thanks Nele!) and city has an incredible beauty. I think these few lines do not do justice to them and all the participants for what they have given. See you again folks!

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