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 / N c 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.
Highlights
It is believed that the dynamics of mesons and baryons should be described by the quantum chromodynamics (QCD), non-Abelian gauge theory of quarks and gluons
In the previous section it was shown in the framework of the NJL2 model that there is a duality between chiral symmetry breaking and pion condensation phenomena
The dualities of the QCD phase diagram, in particular, the duality between chiral symmetry breaking and pion condensation phenomena has been found in the framework of the (1+1)-dimensional QCD
Summary
It is believed that the dynamics of mesons and baryons should be described by the quantum chromodynamics (QCD), non-Abelian gauge theory of quarks and gluons. (iii) It is shown that the duality can be used to produce new results and new phase diagrams (different sections of the phase diagram) As an example, it is showcased how, from the phase structure of dense quark matter with non-zero isospin density (including the possibility of inhomogeneous condensates (phases)), one can obtain, based on the duality only, the phase structure of dense quark matter with chiral imbalance. It is showcased how, from the phase structure of dense quark matter with non-zero isospin density (including the possibility of inhomogeneous condensates (phases)), one can obtain, based on the duality only, the phase structure of dense quark matter with chiral imbalance In this way, from the different regions studied in a number of works, whether one can assemble the whole picture of the phase structure of QCD at finite baryon and isospin density including inhomogeneous phases was explored. As has been pointed out, QCD is hard to deal with, which is why one can try to study the phase structure in a similar but simpler and tractable model (QCD related toy models)
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