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K. G. Klimenko

Publications and source records attributed to K. G. Klimenko.

At least 19 recordsLinked to original sources
arXiv2026

Detailed study of the dual symmetry of dense quark matter within the effective action formalism

The symmetry properties of the phase diagram of dense quark matter composed of $u$ and $d$ quarks with three colors have been investigated in the framework of massless (3+1)-dimensional Nambu--Jona-Lasinio (NJL) and QCD models. It turns out that in the presence of baryon $\mu_B$, isospin $\mu_I$, chiral $\mu_5$ and chiral isospin $\mu_{I5}$ chemical potentials, the Lagrangians of these models are invariant under the so-called dual transformation ${\cal D}$. In this paper, it has been shown that the path integration measure of the corresponding partition functions is also invariant under ${\cal D}$. Consequently, the entire NJL model (or QCD) thermodynamic potentials are dually symmetric. In particular, it means that in the total $(\mu_B,\mu_I,\mu_5,\mu_{I5})$-phase portraits of these models the chiral symmetry breaking (CSB) and charged pion condensation (PC) phases are arranged dually conjugate (or symmetrically) to each other. Dual symmetry between CSB and charged PC phases of quark matter is a fundamental property of massless dense QCD; it should be observed in the framework of any approximation to the QCD phase diagram, and have important implications for studies of the phase structure.

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arXiv2026

Weak dual symmetries of two color QCD phase diagram

The phase diagram of two color QCD under influence of baryon density ($\mu_B$), isospin ($\mu_I$), chiral ($\mu_5$ and $\nu_5$) imbalances is investigated within the framework NJL model approach. This letter establishes the existence of weak dualities in two color quark matter--symmetries revealed when full thermodynamic potential is projected or restricted to specific condensation channels. These dualities provide a unified understanding of two interesting phenomena in the phase diagram: universal catalysis and chameleon effect of chiral chemical potential.

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arXiv2024

Dual symmetries of dense isotopically and chirally asymmetric QCD

In the present paper, the dual symmetries of dense quark matter phase diagram found in some massless three- and two-color NJL models in the mean field approximation have been shown to exist at a more fundamental level as a dual transformations of fields and chemical potentials leaving the Lagrangian invariant. As a result, the corresponding dual symmetries of the full phase diagram can be shown without any approximation. And it has been shown not only in the NJL models, but also in framework of two- and three-color massless QCD itself. This is quite interesting, since one might say that it is not very common to show something completely non-perturbatively in QCD.

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arXiv2024

Charged pion condensation and color superconductivity phenomena in chirally asymmetric dense quark matter

In this paper, the question of the influence of color superconductivity (CSC) on the formation of a phase with condensation of charged pions in dense chirally asymmetric quark matter is studied. We consider it within the framework of the massless NJL model with a diquark interaction channel at zero temperature, but in the presence of baryon $μ_B$, isospin $μ_I$, chiral $μ_{5}$ and chiral isospin $μ_{I5}$ chemical potentials. It has been shown in the mean-field approximation that in the presence of chiral imbalance, when $μ_{5}\ne 0$ and/or $μ_{I5}\ne 0$, CSC phenomenon does not hinder the generation of charged pion condensation in dense quark matter even at largest baryon densities attainable in heavy ion collisions experiments and in cores of neutron stars and its mergers. So charged pion condensation in dense quark matter with chiral imbalance predicted earlier is not in a bit suppressed by the presence of CSC, highlighting the resilience of this phase in dense quark matter. This makes phase structure of dense quark matter even more rich, multifaceted and interesting, and shows that pion condensation in dense quark matter is viable phenomenon to be explored, for example, in intermediate energy heavy ion collisions experiments.

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arXiv2024

Dual symmetries of dense three and two-color QCD and some QCD-like NJL models

In this paper the symmetry properties of the phase diagram of dense quark matter composed of $u$ and $d$ quarks with two or three colors has been investigated in the framework of massless (3+1)-dimensional Nambu--Jona-Lasinio (NJL) and QCD models. It turns out that in the presence of baryon $\mu_B$, isospin $\mu_I$, chiral $\mu_5$ and chiral isospin $\mu_{I5}$ chemical potentials the Lagrangians of these models are invariant under the so-called dual transformations. Consequently, the entire NJL model (or QCD) thermodynamic potentials are dually symmetric. In particular, it means that in the total $(\mu_B,\mu_I,\mu_5,\mu_{I5})$-phase portraits of these models the chiral symmetry breaking (CSB) and charged pion condensation (PC) phases are arranged dually conjugated (or symmetrical) to each other (in the case of three-color models). Whereas in the case of two-color quark matter, these models predict the entire phase structure in which there are dual symmetries between CSB, charged PC and baryon superfluid phases.

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arXiv2023

Dual properties of dense quark matter with color superconductivity phenomenon

In this paper the massless NJL model extended by the diquark interaction channel is considered. We study its phase structure at zero temperature and in the presence of baryon $μ_B$, isospin $μ_I$, chiral $μ_{5}$ and chiral isospin $μ_{I5}$ chemical potentials in the mean-field approximation. It is shown that the model thermodynamic potential, which depends on three order parameters, $M$, $π_1$ and $Δ$ (where $M$, $π_1$, and $Δ$ -- are, respectively, chiral, charged pion and diquark condensates of the model), is symmetric with respect to the (dual) transformation when $M\leftrightarrowπ_1$ and simultaneously $μ_I\leftrightarrowμ_{I5}$. As a result, on the mean-field phase portrait of the model the chiral symmetry breaking (CSB) and charged pion condensation (PC) phases turn out to be dually conjugate with each other, which greatly simplifies the study of the phase portrait of the model. In particular, the duality between CSB and charged PC phases means that in the $(μ_I,μ_{I5})$-phase portrait these phases are mirror-symmetrical with respect to the line $μ_I=μ_{I5}$, which at the same time is the symmetry axis of the color superconducting (CSC) phase. Moreover, it follows from our analysis that chiral $μ_5$ chemical potential promotes the formation of CSC phase in dense quark matter. And together with $μ_{I5}$ it can generates the charged PC phase even at $μ_I=0$.

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arXiv2022

Spontaneous non-Hermiticity in the (2+1)-dimensional Thirring model

Using the Cornwall-Jackiw-Tomboulis effective action $Γ(S)$ for composite operators ($S$ is the full fermion propagator), the phase structure of the massless (2 + 1)-dimensional Thirring model with four-component spinors is investigated in the Hartree-Fock (HF) approximation. In this case both $Γ(S)$ and its stationary (or HF) equation for the full fermion propagator $S$ are calculated in the first order of the bare coupling constant $G$. We have shown that there exist a well-defined dependence of $G\equiv G(Λ)$ on the cutoff parameter $Λ$ under which the HF equation is renormalized. In general, it has two sets, (i) and (ii), of solutions for fermion propagator corresponding to dynamical appearance of different mass terms in the model. In the case of set (i) the mass terms are Hermitian, but the solutions from the set (ii) correspond to a dynamical generation of the non-Hermitiam mass terms, i.e. to a spontaneous non-Hermiticity of the Thirring model. Despite this, the mass spectrum of the quasiparticle excitations of all non-Hermitian ground states is real. In addition, among these non-Hermitian phases there are both $\cP\cT$ symmetrical and non-symmetrical phases. Moreover, in contrast with previous investigations of this effect in other models, we have observed the spontaneous non-Hermiticity phenomenon also in the {\it massive} (2+1)-dimensional Thirring model.

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arXiv2022

Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model

The (2+1)-dimensional generalized massless Thirring model with 4-component Fermi-fields is investigated by the Hartree-Fock method. The Lagrangian of this model is constructed from two different four-fermion structures. One of them takes into account the vector$\times$vector channel of fermion interaction with coupling constant $G_v$, the other - the scalar$\times$scalar channel with coupling $G_s$. At some relation between bare couplings $G_s$ and $G_v$, the Hartree-Fock equation for self-energy of fermions can be renormalized, and dynamical generation of the Dirac and Haldane fermion masses is possible. As a result, phase portrait of the model consists of two nontrivial phases. In the first one the chiral symmetry is spontaneously broken due to dynamical appearing of the Dirac mass term, while in the second phase a spontaneous breaking of the spatial parity $\mathcal P$ is induced by Haldane mass term. It is shown that in the particular case of pure Thirring model, i.e. at $G_s=0$, the ground state of the system is indeed a mixture of these phases. Moreover, it was found that dynamical generation of fermion masses is possible for any finite number of Fermi-fields.

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arXiv2021

Spontaneous non-Hermiticity in the (2+1)-dimensional Gross-Neveu model

Using a nonperturbative approach based on the Cornwall-Jackiw-Tomboulis effective action $Γ(S)$ for composite operators ($S$ is the full fermion propagator), the phase structure of the simplest massless (2 + 1)-dimensional Gross-Neveu model is investigated. We have calculated $Γ(S)$ and its stationary (or Dyson-Schwinger) equation in the first order of the bare coupling constant $G$ and have shown that there exist a well-defined dependence of $G\equiv G(Λ)$ on the cutoff parameter $Λ$, such that the Dyson-Schwinger equation is renormalized. It has three different solutions for fermion propagator $S$ corresponding to possible dynamical appearance of three different mass terms in the model. One is a Hermitian, but two others are non-Hermitian and $\cP\cT$ even or odd. It means that two phases with spontaneous non-Hermiticity can be emerged in the system. Moreover, mass spectrum of quasiparticles is real in these non-Hermitian and $\cP\cT$ even/odd phases.

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arXiv2021

Composite operator approach to dynamical mass generation in the (2+1)-dimensional Gross-Neveu model

Using a nonperturbative approach based on the Cornwall-Jackiw-Tomboulis (CJT) effective action $Γ(S)$ for composite operators, the phase structure of the simplest massless (2 + 1)-dimensional Gross-Neveu model is investigated. We have calculated $Γ(S)$ in the first order of the bare coupling constant $G$ and have shown that there exist three different specific dependences of $G\equiv G(Λ)$ on the cutoff parameter $Λ$, and in each case the effective action and its stationarity equations have been obtained. The solutions of these equations correspond to the fact that three different masses of fermions can arise dynamically and, respectively, three different nontrivial phases can be observed in the model.

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arXiv2021

Influence of chiral asymmetry on phase structure of the two-color quark matter

In this paper the influence of chiral chemical potential $μ_5$ on the phenomenon of diquark condensation and phase structure of dense quark matter altogether is contemplated in the framework of effective two-color and two-flavor Nambu--Jona-Lasinio model. We show that the duality relations, found $μ_5=0$, are also valid for any value of $μ_5\neq0$. Hence the dualities seem to be a real fundamental feature of the phase diagram of two color quark matter, and besides they are a very powerful tool of studying the phase structure. In terms of dualities and the influence on the phase diagram chiral imbalance $μ_5$ stands alone from other chemical potentials. Two regimes in the phase diagram could be discerned, the first one, rather small or moderate values of chemical potentials $μ_B$, $μ_I$ and $μ_{I5}$, where the picture is rather concise and elegant: each of the above phenomena is in one-to-one correspondence with some chemical potential ($μ_{I5}$ induces chiral symmetry breaking, $μ_I$ propels charged pion condensation and $μ_B$ leads to diquark condensation). In this regime chiral chemical potential $μ_5$ does not break this correspondence, it has a property of being universal catalyzer, i.e. it {\it catalyzes/enhances} all the phenomena on equal footing. The feature of chiral imbalance $μ_5$ to catalyze chiral symmetry breaking phenomenon was known before but its catalytic properties appeared to be more universal and it can catalyze also diquark and charged pion condensation. These happen due to the dual properties. In the second regime, when several chemical potentials reach rather large values, one could observe a rather complicated and rich phase structure, and $μ_5$ can be a factor that not so much catalyzes as {\it triggers} rather peculiar phases. For example, it can lead to the formation of diquark condensation at zero baryon chemical potential.

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arXiv2021

The phase structure of two color QCD and charged pion condensation phenomenon

The phase structure of dense quark matter in the two color case has been investigated with nonzero baryon $μ_B$, isospin $μ_I$ and chiral isospin $μ_{I5}$ chemical potentials. %in the framework of Nambu--Jona-Lasinio model with quark-antiquark and quark-quark interaction channels. It has been shown in the mean-field approximation that there exist three dualities, one of them between phases with spontaneous chiral symmetry breaking and condensation of charged pions, found in the three color case. The other two dual symmetries between the phase with condensation of charged pions and the phase with diquark condensation and between chiral symmetry breaking and diquark condensation phenomena. It has been demonstrated that due to the duality properties the phase diagram is extremely symmetric and the whole phase diagram in two color case can be obtained just by dualities from the phase structure of three color case. This shows that the dualities are rather usefull tool. It is shown that chiral imbalance generates charged pion condensation phenomenon in conditions of matter in neutron stars, i. e. electrically neutral and $β$-equilibrated dense quark matter. And that diquark condensation does not prohibit the generation of the charged PC phase by chiral imbalance at least in the two color case.

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arXiv2020

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

In this paper the phase structure of dense baryon matter composed of $u$ and $d$ quarks with two colors has been investigated in the presence of baryon $μ_B$, isospin $μ_I$ and chiral isospin $μ_{I5}$ chemical potentials in the framework of Nambu--Jona-Lasinio model. In the chiral limit, it has been shown that the duality between phases with spontaneous chiral symmetry breaking and condensation of charged pions, found in the three color case, remains valid in the two color case. In addition, it has been shown that there are two more dualities in the phase diagram in two color case, namely (as in the case with $μ_{I5}=0$), at $μ_{I5}\ne 0$ the general $(μ,μ_I,μ_{I5})$-phase portrait of the model has dual symmetry between the phase with condensation of charged pions and the phase with diquark condensation. This duality stays exact even in the physical point, $m_0\ne 0$. And at $m_0=0$ the $(μ,μ_I,μ_{I5})$-phase portrait becomes even more symmetrical, since dual symmetry between phases with spontaneous chiral symmetry breaking and diquark condensation appears. It is shown that due to the dualities the phase diagram is extremely symmetric and has interlacing structure. One can show that the phase portrait of two-color NJL model can be obtained just by duality properties from the results of investigations of three-color NJL model (it was noticed only after the numerical calculations have been performed). Three-color case shares only one duality of the two color one, and one can only see a facet of this enormously symmetric picture in the case of three colors. Using dualities only, it is possible to show that there are no mixed phases (phases with two non-zero condensates). This prediction of dualities is of great use, because for sure it can be shown by the direct calculations but it would be enormously more complicated and time-consuming numerically.

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arXiv2020

Electrical neutrality and $β$-equilibrium conditions in dense quark matter: generation of charged pion condensation by chiral imbalance

The phase diagram of dense quark matter with chiral imbalance is considered with the conditions of electric neutrality and $β$-equilibrium. It has been shown recently that chiral imbalance can generate charged pion condensation in dense quark matter, so it was interesting to verify that this phenomenon takes place in realistic physical scenarios such as electrically neutral matter in $β$-equilibrium, because a window of pion condensation at dense quark matter phase diagram (without chiral imbalance) predicted earlier was closed by the consideration of these conditions at the physical current quark mass. In this paper it has been shown that the charged pion condensation is generated by chiral imbalance in the dense electric neutral quark/baryonic matter in $β$-equilibrium, i. e. matter in neutron stars. It has been also demonstrated that pion condensation is inevitable phenomenon in dense quark matter with chiral imbalance if there is non-zero chiral imbalance in two forms, chiral and chiral isospin one. It seems that in this case pion condensation phase can be hardly avoided by any physical constraint on isopin imbalance and that this conclusion can be probably generalized from neutron star matter to the matter produced in heavy ion collisions or in neutron star mergers. The chiral limit and the physical piont (physical pion mass) has been considered and it was shown that the appearance of pion condensation is not much affected by the consideration of non-zero current quark mass.

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arXiv2020

Dense Baryonic Matter and Applications of QCD Phase Diagram Dualities

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.

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arXiv2020

Dense baryonic matter with chiral imbalance and charged pion condensation

After the first predictions in seventies that in dense nuclear matter, for example, in neutron stars there could be pion condensation phenomenon, it was shown that at least s-wave pion condensation is unlikely to occur in such a medium in different approaches including NJL model consideration with neutrality and $β$-equilibrium condition. Then it has been found a condition that can promote this phenomenon in dense baryonic matter, it is chiral imbalance, so now it is interesting if this generation can survive rather strict requirement of electric neutrality and $β$-equilibrium. Here in this paper the generation of pion condensation in dense baryonic matter by chiral imbalance is investigated. It is shown that electric neutrality and $β$-equilibrium conditions do not spoil this phenomenon and this leads to interesting applications for physics of neutron stars. There are several possible mechanisms of generation of chiral imbalance in dense matter. In a view of latest and forthcoming NICER results and the first observed and possibly new events of neutron star mergers it is rather interesting to explore how possible chiral imbalance in neutron star can influence and change EOS and, hence, mass-radius relation. It is a first step in that direction.

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arXiv2019

Charged pion condensation in dense quark matter: Nambu--Jona-Lasinio model study

In this short review we tried to give an outline of investigations of charged pion condensation (PC) in dense baryonic (quark) matter in the framework of effective Nambu--Jona-Lasinio (NJL) type models. The possibility of charged PC phase in dense quark matter with isospin asymmetry is investigated. First, it is demonstrated that this phase can be realized in the framework of massless NJL model. But the existence of this phase is enormously fragile to the values of current quark mass %.Then, and we show that charged PC phase is forbidden in electrically neutral dense quark matter with $β$-equilibrium when current quark masses are close to their physical value of 5.5 MeV. Nevertheless, then it is shown that in real physical systems there could be conditions promoting the appearance of charged PC phenomenon in dense quark matter, namely, it was shown that if one includes into consideration the fact that system can have finite size, then a dense charged PC phase can be realized there. It was also demonstrated that the possibility of inhomogeneous pion condensate might allow this phase to appear. And more recently it was revealed that there is another interesting factor that can induce a charged PC phase in dense quark matter even without isospin imbalance. It is a chiral imbalance of the system (non-zero difference between densities of left- and right-handed quarks). This results can be interesting in heavy ion collision experiments, where it is expected to get high baryon densities. It is of interest also in the context of the neutron stars, where quark matter might be realized in the core and very high baryon and isospin densities are attained.

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