Dense Baryonic Matter and Applications of QCD Phase Diagram Dualities

Abstract

Recently it has been found that quantum chromodynamics (QCD) phase diagram possesses a duality between chiral symmetry breaking and pion condensation. For the first time this was revealed in the QCD motivated toy model. Then it was demonstrated in effective models as well and new additional dualities being found. We briefly recap the main features of this story and then discuss its applications as a tool to explore the QCD phase structure. The most appealing application is the possibility of getting the results on the QCD phase diagram at large baryon density. Taking the idea from large 1/Nc universalities it was argued that the scenario of circumventing the sign problem with the help of dualities seems plausible. It is also discussed that there is a persistent problem about whether there should be catalysis or anti-catalysis of chiral symmetry breaking by chiral imbalance. One can probably say that the issue is settled after lattice results (first principle approach), where the catalysis was observed. But they used an unphysically large pion mass so it is still interesting to get additional indications that this is the case. It is shown just by the duality property that there exists catalysis of chiral symmetry breaking. So, having in mind our results and the earlier lattice simulations, one can probably claim that this issue is settled. It is demonstrated that the duality can be used to obtain new results. As an example, it is showcased how the phase structure of dense quark matter with chiral imbalance (with possibility of inhomogeneous phases) can be obtained from the knowledge of a QCD phase diagram with isopin asymmetry.

Lattice study of thermodynamic properties of dense QC2D

“…Numerous lattice attempts to overcome the sign problem provide reliable information only in the region of small baryon density [2]. In the absence of straightforward results from lattice simulation of QCD, one applies different analytical approaches to study the ðμ; TÞ phase diagram: mean field approaches [3][4][5][6][7][8][9], the method of Dyson-Schwinger equations and the renormalization group [10][11][12][13], the large-N c approach [14], perturbative QCD [15,16] and others. Although the results obtained theoretically are important, it is rather difficult to estimate the reliability of these predictions.…”

“…The ratio m 2 π Σ qq =μ 2 as a function of chemical potential, where Σ qq is defined in (7).FIG. 6.The ratio −hδð ⃗ E a Þ 2 i=T 4 , defined in(8), as a function of chemical potential. The minus sign is taken since the chromoelectric field decreases in dense matter as compared to the vacuum value.FIG.…”

The dual properties of chiral and isospin asymmetric dense quark matter formed of two-color quarks

“…However, there is another mechanism of chiral asymmetry, which can be realized in dense quark matter in strong magnetic fields (see the discussion in Introduction) and is characterized by the chiral isospin chemical potential µ I5 . And it was shown that chiral isospin imbalance (when µ I5 = 0) promotes the generation of the charged PC phenomenon in dense quark matter [49][50][51][66][67][68][69][70] (see also the recent reviews [7,8] on the topic). Of course, this result can be trusted in the region of relatively low baryon densities of quark matter.…”

“…Thus, interest in the phenomena occurring in dense baryonic matter serves as a trigger for studying QCD-like models and/or theories that are free from the above disadvantages and contribute to a deeper understanding of the properties of the phase diagram of matter at nonzero temperature and baryon density. Among such theories, for example, there are Nambu-Jona-Lasinio (NJL)-like models [1] (see also the reviews [2][3][4][5][6][7][8] and references therein), the QCD and QCD-like models with two-color quarks [9][10][11][12][13][14][15][16][17][18][19][20][21], etc.…”

“…8) where ∆ = ∆ 1 + i∆ 2 and ∆ * = ∆ 1 − i∆ 2 . Compairing the gap equations (3.7) and(3.8) one can see that at m 0 = 0 in the global minimum point (GMP) of the TDP (3.5) we always have π a = 0 (a = 1, 2, 3).…”