*Marco Ruggieri is currently a post-doc fellow at Yukawa Institute for theoretical physics in Kyoto (Japan). Marco has got his PhD at University of Bari in Italy and spent a six months period at CERN. Currently, his main research areas are QCD at finite temperature and high density, QCD behavior in strong magnetic fields and effective models for QCD but you can find a complete CV at his site. So, in view of his expertize I asked him a guest post in my blog to give an idea of the current situation of these studies. Here it is.
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It is well known that Quantum Chromodynamics (QCD) is the most accredited theory describing strong interactions. One of the most important problems of modern QCD is to understand how color confinement and chiral symmetry breaking are affected by a finite temperature and/or a finite baryon density. For what concerns the former, Lattice simulations convince ourselves that both deconfinement and (approximate) chiral symmetry restoration take place in a narrow range of temperatures, see the recent work for a review. On the other hand, it is problematic to perform Lattice simulations at finite quark chemical potential in true QCD, namely with number of color equal to three, because of the so-called sign problem, see here for a recent review on this topic. It is thus very difficult to access the high density region of QCD starting from first principles calculations.

Despite this difficulty, several work has been made to avoid the sign problem, and make quantitative predictions about the shape of the phase diagram of three-color-QCD in the temperature-chemical potential plane, see here again for a review. One of the most important theoretical issues in along this line is the search for the so-called critical endpoint of the QCD phase diagram, namely the point where a crossover and a first order transition line meet. Its existence was suggested by Asakawa and Yazaki (AY) several years ago (see here) using an effective chiral model; in the 2002, Fodor and Katz (FK) performed the first Lattice simulation (see here) in which it was shown that the idea of AY could be realized in QCD with three colors. However, the estimate by FK is affected seriously by the sign problem. Hence, nowadays it is still under debate if the critical endpoint there exists in QCD or not.

After referring to this for a comprehensive review of some of the techniques adopted by the Lattice community to avoid the sign problem and detect the critical endpoint, it is worth to cite an article by Marco Ruggieri, which appeared few days ago on arXiv, in which an exotic possibility to detect the critical endpoint by virtue of Lattice simulations avoiding the sign problem has been detected, see here . We report, after the author permission, the abstract here below:

We suggest the idea, supported by concrete calculations within chiral models, that the critical endpoint of the phase diagram of Quantum Chromodynamics with three colors can be detected, by means of Lattice simulations of grand-canonical ensembles with a chiral chemical potential, , conjugated to chiral charge density. In fact, we show that a continuation of the critical endpoint of the phase diagram of Quantum Chromodynamics at finite chemical potential, , to a critical end point in the temperature-chiral chemical potential plane, is possible. This study paves the way of the mapping of the phases of Quantum Chromodynamics at finite , by means of the phases of a fictitious theory in which is replaced by .

Rajan Gupta (2011). Equation of State from Lattice QCD Calculations arXiv arXiv: 1104.0267v1

Philippe de Forcrand (2010). Simulating QCD at finite density PoS (LAT2009)010, 2009 arXiv: 1005.0539v2

M. Asakawa, & K. Yazaki (1989). Chiral restoration at finite density and temperature Nuclear Physics A, 504 (4), 668-684 DOI: 10.1016/0375-9474(89)90002-X

Z. Fodor, & S. D. Katz (2001). Lattice determination of the critical point of QCD at finite T and \mu JHEP 0203 (2002) 014 arXiv: hep-lat/0106002v2

Marco Ruggieri (2011). The Critical End Point of Quantum Chromodynamics Detected by Chirally

Imbalanced Quark Matter arXiv arXiv: 1103.6186v1

[...] Marco himself proposed a novel approach to get a proof of the critical endpoint to bypass the sign problem (see here). [...]

[...] this implies some relevant physical expectations that a lattice computation should confirm (see here). In this vein, this paper by Yamamoto is a really innovative one facing such kind of computations [...]

[...] Marco pointed out in this blog (see here), due to the lack of knowledge of techniques to manage QCD at low-energies, we are not even able to [...]