Chiral Symmetric Phase Research Articles

Non-Abelian anomalous constitutive relations of a chiral hadronic fluid

We study the constitutive relations of a chiral hadronic fluid in presence of non-Abelian’t Hooft anomalies. Analytical expressions for the covariant currents are obtained at first order in derivatives in the chiral symmetric phase, for both two and three quark flavors in the presence of chiral imbalance. We also investigate the constitutive relations after chiral symmetry breaking at the leading order.

Lack of Debye and Meissner screening in strongly magnetized quark matter at intermediate densities

We study the static responses of cold quark matter in the intermediate baryonic density region (characterized by a chemical potential $\mu$) in the presence of a strong magnetic field. We consider in particular, the so-called Magnetic Dual Chiral Density Wave (MDCDW) phase, which is materialized by an inhomogeneous condensate formed by a particle-hole pair. It is shown, that the MDCDW phase is more stable in the weak-coupling regime than the one considered in the magnetic catalysis of chiral symmetry braking phenomenon (MC$\chi$SB) and even than the chiral symmetric phase that was expected to be realized at sufficiently high baryonic chemical potential. The different components of the photon polarization operator of the MDCDW phase in the one-loop approximation are calculated. We found that in the MDCDW phase there is no Debye screening neither Meissner effect in the lowest-Landau-level approximation. The obtained Debye length depends on the amplitude $m$ and modulation $b$ of the inhomogeneous condensate and it is only different from zero if the relation $| \mu -b| > m$ holds. But, we found that in the region of interest this inequality is not satisfied. Thus, no Debye screening takes place under those conditions. On the other hand, since the particle-hole condensate is electrically neutral, the U(1) electromagnetic group is not broken by the ground state and consequently there is no Meissner effect. These results can be of interest for the astrophysics of neutron stars.

Catalysis of the 〈b̄b〉 Condensate in the Composite Higgs Model

The problem of appearance of quark masses through the mechanism of dynamical breaking of the SU(2)L × U(1)R symmetry of electroweak interactions has been studied within a model with local four-quark interactions, which result in the formation of a 〈tt〉 condensate and composite Higgs bosons. We show that this process catalyzes bb condensation in the presence of an arbitrarily weak’ t Hooft interaction. The spectrum of composite scalar excitations has been calculated. An expression obtained for the mass of a standard Higgs boson significantly improves the agreement of the top-condensation model with the experiment. It has been shown that the standard Higgs boson under the Nambu sum rules should have three partners with the same mass of about 245 GeV and different electric charges. The possibility of a transition of the system to a chiral symmetric phase, which is accompanied by the corresponding change in the spectrum of elementary excitations, is discussed.

Topology in the SU(Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology

The axion is one of the more interesting candidates to make the dark matter of the universe, and the axion potential plays a fundamental role in the determination of the dynamics of the axion field. Moreover, the way in which the U(1)A anomaly manifests itself in the chiral symmetry restored phase of QCD at high temperature could be tested when probing the QCD phase transition in relativistic heavy ion collisions. With these motivations, we investigate the physical consequences of the survival of the effects of the U(1)A anomaly in the chiral symmetric phase of QCD, and show that the free energy density is a singular function of the quark mass m, in the chiral limit, and that the σ and π susceptibilities diverge in this limit at any T ≥ Tc. We also show that the difference between the π and δ susceptibilities diverges in the chiral limit at any T ≥ Tc, a result that can be contrasted with the existing lattice calculations; and discuss on the generalization of these results to the Nf ≥ 3 model.

Topology in the SU(Nf) chiral symmetry restored phase of unquenched QCD and axion cosmology. II.

We investigate the physical consequences of the survival of the effects of the U(1)_A anomaly in the chiral symmetric phase of QCD, and show that the free energy density is a singular function of the quark mass m, in the chiral limit, and that the $\sigma$ and $\bar\pi$ susceptibilities diverge in this limit at any $T\ge T_c$. We also show that the difference between the $\bar\pi$ and $\bar\delta$ susceptibilities diverges in the chiral limit at any $T\ge T_c$, a result which seems to be excluded by recent results of Tomiya et al. from numerical simulations of two-flavor QCD. We also discuss on the generalization of these results to the $N_f\ge 3$ model.

Spontaneous generation of localCPviolation and inverse magnetic catalysis

In the chiral symmetric phase, the polarized instanton--anti-instanton molecule pairing induces a nontrivial repulsive interaction in the iso-scalar axial-vector channel. As a consequence, one unusual property is observed that in the chiral restoration phase, there is a first order phase transition for the spontaneous generation of local CP violation and chiral imbalance. Furthermore, it is found that external magnetic fields will lower the critical temperature for the local CP-odd phase transition and catalyze the chiral imbalance, which destroys the chiral condensate with pairing quarks between different chiralities. A reasonable strength of the repulsive interaction in the iso-scalar axial-vector channel can naturally explain the inverse magnetic catalysis around the critical temperature under external magnetic fields.

Chiral symmetry in SU(Nc) gauge theories at high density

SU(Nc) lattice gauge theories with Nf flavors of massless staggered fermions are studied in the presence of quark chemical potential μ. A recent exact result that in the strong coupling limit (vanishing inverse gauge coupling β) and for sufficiently large μ the theory is in a chiral symmetric phase is here extended into the finite gauge coupling region. These and similar results are obtained by means of a cluster expansion which combines a fermion spacelike hopping expansion and a strong coupling plaquette expansion. The cluster expansion is shown to converge for sufficiently large μ and small β at any temperature T. All expectations of chirally noninvariant local fermion operators vanish identically, or, equivalently, their correlations cluster exponentially within the expansion. This implies the absence of spontaneous breaking of (any part of) the global chiral symmetries in the theory. The resulting phase at low T may be described as a "quarkyonic" matter phase. There is thus absence of any superfluidity or color superconductivity in this strong coupling regime. Implications for the phase diagram of SU(Nc) theories in the region of large chemical potential are discussed.

Magnetic properties of four dimensional fermions

We investigate the Sakai-Sugimoto model at nonzero baryon chemical potential in a background magnetic field in the chiral symmetric phase. We find that a new form of baryonic matter shows up, and we investigate its properties. We find a generated axial current, a reduction in the amount of charge participating in dissipative interactions and a metamagnetic like phase transition at low temperature.

Magnetic Catalysis Versus Magnetic Inhibition

We discuss the fate of chiral symmetry in an extremely strong magnetic field B. We investigate not only quark fluctuations but also neutral meson effects. The former enhances the chiral-symmetry breaking at finite B according to the magnetic catalysis, while the latter suppresses the chiral condensate once B exceeds the scale of the hadron structure. Using a chiral model, we demonstrate how neutral mesons are subject to the dimensional reduction and the low dimensionality favors the chiral-symmetric phase. We point out that this effect, the magnetic inhibition, can be a feasible explanation for recent lattice-QCD data indicating the decreasing behavior of the chiral-restoration temperature with increasing B.

Chiral symmetry restoration, the eigenvalue density of the Dirac operator, and the axial U(1) anomaly at finite temperature

We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac operator, which ensures the exact "chiral" symmetry at finite lattice spacings. Studying multi-point correlation functions in various channels and taking their thermodynamical limit (and then taking the chiral limit), we obtain stronger constraints than those found in the previous studies: both the eigenvalue density at the origin and its first and second derivatives vanish in the chiral limit of 2 flavor QCD. In addition we show that the axial U(1) anomaly becomes invisible in susceptibilities of scalar and pseudo scalar mesons, suggesting that the 2nd order chiral phase transition with the O(4) scaling is not realized in 2 flavor QCD. Possible lattice artifacts when non-chiral lattice Dirac operator is employed are briefly discussed.

Characteristic of chiral phase transition inQED3at zero density

Based on the truncated Dyson-Schwinger equation for the fermion propagator, the Cornwall-Jackiw-Tomboulis effective potential near the critical point is investigated. We show that, at zero temperature, the system undergoes a continuous phase transition into the chiral symmetric phase at a critical number of fermion flavors, while undergoing a second-order phase transition at high temperature.

Structure function of holographic quark-gluon plasma: Sakai-Sugimoto model versus its noncritical version

Motivated by recent studies of deep inelastic scattering (DIS) off the $\mathcal{N}=4$ super-Yang-Mills (SYM) plasma, holographically dual to $AdS_5\times S^5$ black hole, we in this note use the spacelike flavor current to probe the internal structure of one holographic quark-gluon plasma, which is described by the Sakai-Sugimoto model at high temperature phase (i.e., the chiral symmetric phase). The plasma structure function is extracted from the retarded flavor current-current correlator. Our main aim here is to explore the effect of non-conformality on these physical quantities. As usual, our study is under the supergravity approximation and the limit of large color number. Although the Sakai-Sugimoto model is non-conformal, which makes the calculations more involved than the well-studied $\mathcal {N}$=4 SYM case, the result seems to indicate that the non-conformality has little essential effect on the physical picture of the internal structure of holographic plasma, which is consistent with the intuition from the asymptotic freedom of QCD at high energy. While the physical picture underlying our investigation is same as the DIS off the $\mathcal {N}$=4 SYM plasma with(out) flavor, the plasma structure functions are quantitatively different, especially their scaling dependence on the temperature, which can be recognized as model-dependent. As a comparison, we also do the same analysis for the non-critical version of the Sakai-Sugimoto model which is conformal in the sense that it has a constant dilaton vacuum. The result for this non-critical model is much similar to the conformal $\mathcal{N}=4$ SYM plasma. We therefore attribute the above difference to the effect of non-conformality of the Sakai-Sugimoto model.

Spectral function and quark diffusion constant in non-critical holographic QCD

Motivated by recent studies of intersecting D-brane systems in critical string theory and phenomenological AdS/QCD models, we present a detailed analysis for the vector and scalar fluctuations in a non-critical holographic QCD model in the high temperature phase, i.e., the chiral symmetric phase. This model is described by N f pairs of D4 and D 4 ¯ probe branes in a non-critical AdS 6 black hole background. Focusing on the hydrodynamic as well as the high frequency limit, we analytically obtain spectral functions for vector and scalar modes on the flavor probe. Then we extract the light quark diffusion constant for flavor current using three different methods and find that different methods give the same results. We also compute the heavy quark diffusion constant for comparison with the light quark case.

Thermal conductivity of the quark matter

We discuss the thermal conductivity of quark matter in the framework of the Kubo formula and the Nambu–Jona-Lasinio model. Using the quasi-particle random phase approximation, the thermal conductivity can be expressed by the quadratic form of the quark spectral function in the chiral symmetric phase. Its numerical value is calculated as a function of the mean free path of quarks assuming the Breit–Wigner type for the spectral function. The calculated thermal conductivity is rather large in contrast to the small shear viscosity. It is shown that the ratio of the thermal conductivity to the shear viscosity is independent of the temperature but is a decreasing function of the chemical potential.

Magnetic properties of dense holographic QCD

We investigate the Sakai-Sugimoto model at nonzero baryon chemical potential in a background magnetic field both in the confined phase and in the deconfined phase with restored chiral symmetry. In this case the 8-brane Chern-Simons term becomes important. In the confined phase it generates a gradient of the pseudoscalar ``pion,'' which carries a nonvanishing baryon charge. Above a critical value of the chemical potential there is a second-order phase transition to a mixed phase which includes also ordinary baryonic matter. However, at fixed baryon charge density the matter is purely pion-gradient above a critical magnetic field. In the deconfined chiral-symmetric phase at nonzero chemical potential the magnetic field induces an axial current. We also compute the magnetization of the baryonic matter and find that it is paramagnetic in all three phases but with nonlinear behavior at a large magnetic field.

The phase structure of Einstein–Cartan theory

In the Einstein–Cartan theory of torsion-free gravity coupling to massless fermions, the four-fermion interaction is induced and its strength is a function of the gravitational and gauge couplings, as well as the Immirzi parameter. We study the dynamics of the four-fermion interaction to determine whether effective bilinear terms of massive fermion fields are generated. Calculating one-particle-irreducible two-point functions of fermion fields, we identify three different phases and two critical points for phase transitions characterized by the strength of four-fermion interaction: (1) chiral symmetric phase for massive fermions in strong coupling regime; (2) chiral symmetric broken phase for massive fermions in intermediate coupling regime; (3) chiral symmetric phase for massless fermions in weak coupling regime. We discuss the scaling-invariant region for an effective theory of massive fermions coupled to torsion-free gravity in the low-energy limit.

Shear viscosity of the quark matter

We discuss shear viscosity of the quark matter by using the Kubo formula and the Nambu–Jona–Lasinio model. It is shown that the leading term of 1/N expansion for the shear viscosity is equivalent to the quasi-particle random phase approximation. Using this approximation, we obtain a formula that the shear viscosity is expressed by the quadratic form of the quark spectral function in the chiral symmetric phase. If we assume the Breit–Wigner type for the spectral function, the shear viscosity is evaluated as a function of the imaginary part of the quark self-energy, which is related to the mean-free path of the quark. It is pointed out that the quark matter seems to be a perfect liquid for the mean free path <2 fm.

Quasi-Quark Spectrum in the Chiral Symmetric Phase from the Schwinger-Dyson Equation

We non-perturbatively study the fermion spectrum in the chiral symmetric phase from the Schwinger-Dyson equation with the Feynman gauge, in which we perform an analytic continuation of the solution on the imaginary time axis to the real time axis with a method employing an integral equation. It is shown that the fermion spectrum has two peaks, which correspond to the normal quasi-fermion and the plasmino, although these peaks in the strong coupling region are very broad, owing to multiple scatterings with gauge bosons. We find that the thermal mass of the quasi-fermion saturates at some value of the gauge coupling, beyond which the thermal (pole) mass satisfies $M \sim T$, independently of the value of the gauge coupling. We also comment on the appearance of a three-peak structure in the fermion spectrum as a non-perturbative effect.

The color flavor locked phase in the chromodielectric model and quark stars

Recent results obtained in the Chromodielectric Model (CDM) have shown that strange quark matter at very high densities may appear in two phases, namely a chiral broken and a chiral symmetric phase, which may not be absolutely stable. In the chiral symmetric phase, the abundance of the quarks flavors u, d and s is the same and there are no electrons. In this paper we study an extended version of the Chromodielectric model (CDM) with a BCS quark pairing implemented, and analyze the superconducting color flavor locked phase. We show that the inclusion in the free energy density of a negative term of the diquark condensate guarantees the stability of quark matter. We also analyze the phase transition between matter described by different equations of state and only find a first order transition, at a very low pressure, from the CFL phase to the unpaired strange quark matter, which opens the possibility for a quark-hadron phase transition. Our study has implications in astrophysics, in particular regarding the formation and the structure of compact quark stars. We explicitly show that CFL stars can be absolutely stable and more compact than strange stars.

Behavior of Vacuum Polarization of Gauge-Boson and WavefunctionRenormalization Factor of Fermion in Different Phases of QED3

We investigate the behavior of the vacuum polarization ofthe gauge-boson Π and the wave-function renormalizationfactor of the fermion A in QED3, using the coupledDyson–Schwinger equations for the gauge-boson and fermionpropagator. Using several different ansätze for thefermion-gauge-boson vertex, we find that the wave-functionrenormalization factor A and especially the vacuum polarizationΠ have different behaviors in the dynamical chiral symmetrybreaking phase and in the chiral symmetric phase and hence inthe phenomenological applications of QED3 one should choosedifferent forms of gauge-boson propagator for these two phases.We also find that when adopting a specific ansätze of thefermion-gauge-boson vertex (ansätze (3)) the vacuum polarizationfunction equals its one-loop perturbative result in the chiralsymmetric phase. This fact suggests that in QED3 the Wigner vacuumcorresponds to the perturbative vacuum.