Chiral Symmetry Breaking Phase Research Articles

Competition and duality correspondence between inhomogeneous fermion-antifermion and fermion-fermion condensations in theNJL2model

We investigate the possibility of spatially homogeneous and inhomogeneous chiral fermion-antifermion condensation and superconducting fermion-fermion pairing in the ($1+1$)-dimensional model by Chodos et al. [Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature $T$, electric charge chemical potential $\ensuremath{\mu}$ and chiral charge chemical potential ${\ensuremath{\mu}}_{5}$. It is shown that at ${G}_{1}<{G}_{2}$, where ${G}_{1}$ and ${G}_{2}$ are the coupling constants in the fermion-antifermion and fermion-fermion channels, the $(\ensuremath{\mu},{\ensuremath{\mu}}_{5})$-phase structure of the model is in a one-to-one correspondence with the phase structure at ${G}_{1}>{G}_{2}$ (called duality correspondence). Under the duality transformation the (inhomogeneous) chiral symmetry breaking (CSB) phase is mapped into the (inhomogeneous) superconducting (SC) phase and vice versa. If ${G}_{1}={G}_{2}$, then the phase structure of the model is self-dual. Nevertheless, the degeneracy between the CSB and SC phases is possible in this case only when there is a spatial inhomogeneity of condensates.

Inhomogeneous phases in the quark-meson model with vacuum fluctuations

Inhomogeneous chiral-symmetry breaking phases at non-vanishing chemical potential and temperature are studied within a two-flavor quark-meson model in the chiral limit. The analysis is performed beyond the standard mean-field approximation by taking into account the Dirac-sea contributions of the quarks. Compared with the case where the Dirac sea is neglected, we find that the inhomogeneous phase shrinks, but in general does not disappear. It is shown within a Ginzburg-Landau analysis that the Lifshitz point of the inhomogeneous phase coincides with the tricritical point if the ratio between sigma-meson and constituent quark mass in vacuum is chosen to be $m_\sigma/M = 2$, corresponding to the fixed mass ratio in the Nambu--Jona-Lasinio model. In the present model, however, this ratio can be varied, offering the possibility to separate the two points. This is confirmed by our numerical calculations, which demonstrate a strong sensitivity of the size of the inhomogeneous phase on $m_\sigma$. Finally, we uncover a general instability of the model with respect to large wave numbers of the chiral modulations, which calls for further improvements beyond the present approximation.

S-duality of nonsupersymmetric gauge theories

We propose a method for constructing pairs of nonsupersymmetric gauge theories related by S-duality. Starting from a known S-duality of supersymmetric theories realized on the worldvolume of D3 branes in type IIB string theory, a new duality is obtained by replacing the D3-branes with antibranes. Large classes of dual pairs of nonsupersymmetric theories can be obtained in this way, with different interactions and matter content (chiral and vector-like). The approach is illustrated on gauge theories realized on three-branes and fractional branes probing orbifold singularities. The duality sheds light on the dynamics of gauge theories and their possible infrared phases by providing concrete magnetic dual descriptions of strongly coupled theories. Some of the models share various properties with QCD, including confinement and chiral symmetry breaking. More generally, these theories feature fermions in multiple two-index representations and could realize intriguing phases such as a free magnetic phase with chiral symmetry breaking or mixed phases where an interacting fixed point coexists with a confining phase.

A novel (2+1)-dimensional model of chiral symmetry breaking

We propose a new model of flavour chiral symmetry breaking in a (2+1)-dimensional defect gauge theory of strongly coupled fermions by introducing probe D5/anti-D5-flavour branes on the conifold. After working out the flavour brane embeddings at zero temperature, we thoroughly investigate the spectra of small fluctuations on the world volume of the flavour branes (meson spectrum) and conclude that they are free of tachyons. Thus the proposed probe brane embedding is stable. Moreover, we introduce finite temperature and an external magnetic field and study the thermodynamics of the resulting configurations. Namely, we compute the free energies, entropies, heat capacities and magnetisations. The results are used to establish a detailed phase diagram of the model. We find that the effect of magnetic catalysis of chiral symmetry breaking is realised in our model and show that the meson-melting phase transition coincides with the chiral symmetry breaking phase transition. Furthermore, we show that the model is in a diamagnetic phase.

Inhomogeneous chiral symmetry breaking phases

We investigate inhomogeneous chiral symmetry breaking phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model, concentrating on phases with one-dimensional modulations. It is found that the first-order transition line in the phase diagram of homogeneous phases gets completely covered by an inhomogeneous phase which is bordered by second-order transition lines. The inhomogeneous phase turns out to be remarkably stable when vector interactions are included.

Nucleons at finite temperature and low density in Faddeev equation approach

We study some properties of nucleons with a simplified version of a Faddeev equation at finite temperature and baryon chemical potential in the framework of the Nambu--Jona-Lasinio model. By taking diquark-quark bubble summation, we constructed the nucleon propagator and calculated the dynamical masses of the diquark and the nucleon in the pole approximation. We show that diquarks can survive as resonant states in the chiral symmetry restored phase at high temperature, and that nucleons are restricted in the chiral symmetry broken phase at low temperature. The phase diagram of the strongly interacting matter is then given.

Inhomogeneous islands and continents in the Nambu--Jona-Lasinio model

We present some recent developments in our study of inhomogeneous chiral symmetry breaking phases in the Nambu--Jona-Lasinio model. First, we investigate different kinds of one- and two-dimensional spatial modulations of the chiral condensate within the inhomogeneous island and compare their free energies. Next, we employ the Polyakov-loop extended version of the model to study the effects of varying the number of colors on the inhomogeneous region. Finally, we discuss the properties of an inhomogeneous continent which appears in our model at higher chemical potentials, and analyze its origin.

CHIRAL MAGNETIC EFFECT AND QCD PHASE TRANSITIONS WITH EFFECTIVE MODELS

We study the influence of the chiral phase transition on the chiral magnetic effect. The chiral electric current density along the magnetic field, the electric charge difference between on each side of the reaction plane, and the azimuthal charged-particle correlations as functions of the temperature during the QCD phase transitions are calculated. It is found that with the decrease of the temperature, the chiral electric current density, the electric charge difference, and the azimuthal charged-particle correlations all get a sudden suppression at the critical temperature of the chiral phase transition, because the large quark constituent mass in the chiral symmetry broken phase quite suppresses the axial anomaly and the chiral magnetic effect. We suggest that the azimuthal charged-particle correlations (including the correlators divided by the total multiplicity of produced charged particles which are used in current experiments and another kind of correlators not divided by the total multiplicity) can be employed to identify the occurrence of the QCD phase transitions in RHIC energy scan experiments.

Chiral phase transitions and quantum critical points of the D3/D7(D5) system with mutually perpendicular E and B fields at finite temperature and density

We study chiral symmetry restoration with increasing temperature and density in gauge theories subject to mutually perpendicular electric and magnetic fields using holography. We determine the chiral symmetry breaking phase structure of the D3/D7 and D3/D5 systems in the temperature-density-electric field directions. A magnetic field may break the chiral symmetry and an additional electric field induces Ohm and Hall currents as well as restoring the chiral symmetry. At zero temperature the D3/D5 system displays a line of holographic BKT phase transitions in the density-electric field plane, while the D3/D7 system shows a mean-field phase transition. At intermediate temperatures, the transitions in the density-electric field plane are of first order at low density, transforming to second order at critical points as density rises. At high temperature the transition is only ever first order.

Peak of Chiral Susceptibility and Chiral Phase Transition in QED3

A general expression for the scalar susceptibility in QED3 is given. We adopt the Dyson-Schwinger equation for the fermion propagator to solve χc within a range of the number of fermion flavors, N, in chiral symmetry breaking phase. We show that the scalar susceptibility has a peak and the corresponding N is less than the critical number of fermion flavors for chiral symmetry.

Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases

We investigate the role of the isoscalar vector interaction and the dynamics of the Polyakov loop on inhomogeneous phases in the phase diagram of the two-flavor Nambu-Jona--Lasinio (NJL) model. Thereby we concentrate on phases with a one-dimensional modulation, explicitly domain-wall solitons and, for comparison, the chiral spiral. While the inclusion of the Polyakov loop merely leads to quantitative changes compared to the original NJL model, the presence of a repulsive vector-channel interaction has significant qualitative effects: Whereas for homogeneous phases the first-order phase transition gets weakened and eventually turns into a second-order transition or a cross-over, the domain of inhomogeneous phases is less affected. In particular the location of the Lifshitz point in terms of temperature and density is not modified. Consequently, the critical point disappears from the phase diagram and only a Lifshitz point (showing a different critical behavior) remains. As a result, susceptibilities remain finite.

Viscosities in chiral symmetry breaking phase

In the chiral symmetry breaking phase described by the NJL model at quark level, along with the chiral symmetry restoration the ratio of shear viscosity to entropy density η/s drops down monotonously and reaches the minimum at the critical point, while the ratio of bulk viscosity to entropy density ζ/s behaves oppositely.

Phases of Holographic QCD

We investigated the Sakai-Sugimoto model of large N QCD at nonzero temperature and baryon chemical potential and in the presence of background electric and magnetic fields. We studied the holographic representation of baryons and the deconfinement, chiral-symmetry breaking, and nuclear matter phase transitions. In a background electric field, chiral-symmetry breaking corresponds to an insulator-conductor transition. A magnetic field both catalyzes chiral-symmetry breaking and generates, in the confined phase, a pseudo-scalar gradient or, in the deconfined phase, an axial current. The resulting phase diagram is in qualitative agreement with studies of hot, dense QCD.

Phase diagram of neutral quark matter in nonlocal chiral quark models

We consider the phase diagram of two-flavor quark matter under neutron star constraints for two nonlocal, covariant quark models within the mean-field approximation. In the first case (Model I) the nonlocality arises from the regularization procedure, motivated by the instanton liquid model, whereas in the second one (Model II) a separable approximation of the one-gluon exchange interaction is applied. We find that Model II predicts a larger quark mass gap and a chiral symmetry breaking (CSB) phase transition line which extends 15--20% further into the phase diagram spanned by temperature ($T$) and chemical potential ($\ensuremath{\mu}$). The corresponding critical temperature at $\ensuremath{\mu}=0$, ${T}_{c}(0)\ensuremath{\simeq}140\text{ }\text{ }\mathrm{MeV}$, is in better accordance to recent lattice QCD results than the prediction of the standard local NJL model, which exceeds 200 MeV. For both Model I and Model II we have considered various coupling strengths in the scalar diquark channel, showing that different low-temperature quark matter phases can occur at intermediate densities: a normal quark matter (NQM) phase, a two-flavor superconducting (2SC) quark matter phase and a mixed 2SC-NQM phase. Although in most cases there is also a gapless 2SC phase, this occurs in general in a small region at nonzero temperatures, thus its effect should be negligible for compact star applications.

Dyson–Schwinger equation and quantum phase transitions in massless QCD

We study the stability of the highest symmetric solution (Wigner-solution) of Dyson–Schwinger equations in chiral limit and at zero temperature. Our results confirm that if the chemical potential is not very large, the QCD vacuum is in the chiral symmetry breaking phase and the quantum phase-transition of the chiral symmetry restoration is in first order. Meanwhile, it seems that there is not competition between chiral breaking phase and color superconductivity phase since the color superconductivity phase appears only if the chemical potential is very large. Moreover, we propose that chiral symmetry breaking arises from the positive feedback with respect to the mass perturbation.

Counterexamples to the correlated stability conjecture

We demonstrate explicit counter-examples to the Correlated Stability Conjecture (CSC), which claims that the horizon of a black brane is unstable precisely if that horizon has a thermodynamic instability, meaning that its matrix of susceptibilities has a negative eigenvalue. These examples involve phase transitions near the horizon. Ways to restrict or revise the CSC are suggested. One of our examples shows that N=1* gauge theory has a second order chiral symmetry breaking phase transition at a temperature well above the confinement scale.

Gapless Hartree-Fock resummation scheme for theO(N)model

A modified selfconsistent Hartree-Fock approximation to the lambda*phi^4 theory with spontaneously broken O(N) symmetry is proposed. It preserves all the desirable features, like conservation laws and thermodynamic consistency, of the selfconsistent Dyson scheme generated from a 2PI functional, also known as the Phi-derivable scheme, while simultaneously respecting the Nambu-Goldstone theorem in the chiral-symmetry broken phase. Various approximate resummation schemes are discussed.

Superluminal pions in a hadronic fluid

We study the propagation of pions at finite temperature and finite chemical potential in the framework of the linear sigma model with 2 quark flavors and ${N}_{c}$ colors. The velocity of massless pions in general differs from that of light. One-loop calculations show that in the chiral symmetry broken phase pions, under certain conditions, propagate faster than light.

Effects of vector coupling on chiral and color-superconducting phase transitions - interplay among the scalar, pairing and vector interaction

We investigate effects of the vector interaction appearing in chiral effective Lagrangians on the chiral and color superconducting (CSC) phase transitions using Nambu-Jona-Lasinio model. It is shown that the repulsive density-density interaction coming from the vector term enhances competition between the chiral symmetry breaking (κSB) and CSC phase transition: When the vector coupling is increased, the first order transition between the κSB and CSC phase becomes weaker, and the coexisting phase in which both the chiral and color-gauge symmetries are dynamically broken comes to exisit in a wider region in the T- μ plane. We find that the critical line of the first order transition can have two endpoints for an intermediate range of the vector coupling.

Chiral symmetry breaking, color superconductivity and quark matter phase diagram: a variational approach

We discuss in this note simultaneous existence of chiral symmetry breaking and color superconductivity at finite temperature and density in a Nambu–Jona–Lasinio type model. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. There exist nontrivial solutions to the gap equations at finite densities with both quark–antiquark as well as diquark condensates for the “ground” state. However, such a phase is thermodynamically unstable with the pressure being negative in this region. We also compute the equation of state, and obtain the structure of the phase diagram in the model.