Chiral Symmetry Breaking Phase Research Articles

A domain wall and chiral edge currents in holographic chiral phase transitions

We investigate spatially inhomogeneous solutions in a top-down holographic model: the D3/D7 model which provides a holographic description of the chiral phase transition for a finite external magnetic field, chemical potential, and temperature. We numerically find a domain wall (or kink) solution in the three dimensional space, which incorporates between the chiral symmetry broken phase at the spatial infinity, under the homogeneous sources. Along with the inhomogeneity of the chiral condensate, the charge density is also spatially modulated. The modulated charge density and finite magnetic field lead to the chiral edge current close to the domain wall. We explore the dependences of those profiles on the chemical potential and temperature near the first and second order phase transition points. Our results indicate that the inhomogeneous solutions we found are in good agreement with those obtained by the Ginzburg-Landau theory in the vicinity of the transition points.

QCD Kondo effect for single heavy quark in chiral-symmetry broken phase

We consider the quantum chromodynamics (QCD) Kondo effect for a single heavy quark in quark matter composed of light quarks with chiral symmetry breaking. Introducing several spinor structures in QCD Kondo condensates, i.e., particle-projected condensate, antiparticle-projected condensate, and normal condensate without projection, we calculate the attractive energy gained by the heavy quark within the mean-field approximation in the path-integral formalism. We show that the normal condensate is favored at low density and the particle-projected condensate is favored at high density, when the light quark has a nonzero mass. We interpret such a density-dependent transition between the two condensates in terms of the Kondo resonances. Published by the American Physical Society 2024

Probing exotic phases via stochastic gravitational wave spectra

Abstract Stochastic backgrounds of gravitational waves (GWs) from the pre-BBN era offer a unique opportunity to probe the universe beyond what has already been achieved with the Cosmic Microwave Background (CMB). If the source is short in duration, the low frequency tail of the resulting GW spectrum follows a universal frequency scaling dependent on the equation of state of the universe when modes enter the horizon. We demonstrate that the distortion of the equation of state due to massive particles becoming non-relativistic can lead to an observable dip in the GW spectrum. To illustrate this effect, we consider a first order chiral symmetry breaking phase transition in the weak-confined Standard Model (WCSM). The model features a large number of pions and mostly elementary fermions with masses just below the critical temperature for the phase transition. These states lead to a 20% dip in the GW power. We find potential sensitivity to the distortions in the spectrum to future GW detectors such as LISA, DECIGO, BBO, and μAres.

Anisotropic pressure of magnetized quark matter with anomalous magnetic moment

We investigate magnetic field $(eB)$ dependence of constituent quark mass, the longitudinal and transverse pressure as well as the magnetization and magnetic susceptibility of strongly interacting quark matter. We employ the two-flavor Polyakov Nambu--Jona-Lasinio model with the inclusion of the anomalous magnetic moment (AMM) of the quarks at finite temperature ($T$) and finite quark chemical potential $({\ensuremath{\mu}}_{q})$ capturing different stages of chiral phase transition. We find that the transverse pressure, magnetization, and magnetic susceptibility become highly oscillatory for large values of $eB$ in the chiral symmetry broken phase. However, the oscillations cease to occur at higher values of $T$ and ${\ensuremath{\mu}}_{q}$ when chiral symmetry is (partially) restored and the anisotropic nature of the pressure becomes significant even at smaller values of $eB$. As the inclusion of AMM of the quarks leads to inverse magnetic catalysis of the transition temperature, we observe that the variations of transverse pressure, magnetization, and magnetic susceptibility are significantly modified in the vicinity of the chiral transition temperature. Furthermore, above the chiral transition temperature the magnetic susceptibility is found to remain positive for a wide range of $eB$, indicating a paramagnetic character of the strongly interacting quark matter. Finally, we have also examined the magnetism of strongly interacting matter in the quarkyonic phase. The obtained results could be useful for a magnetohydrodynamic evolution of hot and dense matter created in heavy-ion collisions.

Electromagnetic spectral functions in hot and dense chirally imbalanced quark matter

The photon self-energy from chirally imbalanced quark matter is evaluated at finite temperature and density using the real time formulation of thermal field theory. The analytic structure is explored in detail exposing the cut structure which corresponds to a variety of physical scattering and decay processes in the medium and their thresholds. The mass of the quarks in the chiral symmetry broken phase are obtained from the gap equation of the Nambu--Jona-Lasinio model. It is found that, in presence of finite chiral chemical potential, the chiral condensate tends to get stronger at low temperatures while the opposite is observed at high temperature values. A continuous spectrum is obtained for the electromagnetic spectral function and this is purely a finite chiral chemical potential effect.

Thermomagnetic modification of the anomalous magnetic moment of quarks using the NJL model

The effective photon-quark-antiquark ($\gamma q \overline{q}$) vertex function is evaluated at finite temperature in the presence of an arbitrary external magnetic field using the two-flavor gauged Nambu--Jona-Lasinio (NJL) model in the mean field approximation. The lowest order diagram contributing to the magnetic form factor and the anomalous magnetic moment (AMM) of the quarks is calculated at finite temperature and external magnetic field using the imaginary time formalism of finite temperature field theory and the Schwinger proper time formalism. The Schwinger propagator including all the Landau levels with non-zero AMM of the dressed quarks is considered while calculating the loop diagram. Using sharp as well as smooth three momentum cutoff, we regularize the UV divergences arising from the vertex function and the parameters of our model are chosen to reproduce the well known phenomenological quantities at zero temperature and zero magnetic field, such as pion-decay constant ($f_\pi$), vacuum quark condensate, vacuum pion mass ($m_\pi$) as well as the magnetic moments of proton and neutron. We then study the temperature and magnetic field dependence of the AMM and constituent mass of the quark. We found that, the AMM as well as the constituent quark mass are large at the chiral symmetry broken phase in the low temperature region. Around the pseudo-chiral phase transition they decrease rapidly and at high temperatures both of them approach vanishingly small values in the symmetry restored phase.

A bestiary of black holes on the conifold with fluxes

We present a comprehensive analysis of the black holes on warped deformed conifold with fluxes in Type IIB supergravity. These black holes realize the holographic dual to thermal states of the mathcal{N} = 1 supersymmetric SU(N) × SU(N + M) cascading gauge theory of Klebanov et al. [1, 2] on round S3. There are three distinct mass scales in the theory: the strong coupling scale Λ of the cascading gauge theory, the compactification scale μ = 1/L3 (related to the S3 radius L3) and the temperature T of a thermal state. Depending on Λ, μ and T, there is an intricate pattern of confinement/deconfinement (Hawking-Page) and the chiral symmetry breaking phase transitions. In the S3 → ℝ3 decompactification limit, i.e., μ → 0, we recover the Klebanov-Tseytlin [3] and the Klebanov-Strassler [4] black branes.

Chiral symmetry breaking and chemical equilibrium in heavy-ion collisions

We examine the thermalization of an ensemble of the octet of pseudoscalar mesons, in the isospin symmetric limit, whose interactions are constrained through chiral symmetry, unitarity, and measurements. The reaction amplitudes generate all resonances up to masses of about 2 GeV, with twelve input parameters, namely f_pi, three masses, and eight low energy constants (LECs) of chiral perturbation theory. In linear response theory, we find that matter takes an extremely long time to thermalize. These long relaxation times are directly related to the fact that these mesons are pseudo-Goldstone bosons of chiral symmetry breaking. This result indicates that fireballs created with zero baryon number in heavy-ion collisions will drop out of chemical equilibrium once they enter the chiral symmetry broken phase.

Response functions of hot and dense matter in the Nambu-Jona-Lasino model * * Supported by the National Natural Science Foundation of China (11775123, 11890712, 11747312, 11475062) and the National Key R&D Program of China (2018YFA0306503)

We investigate current-current correlation functions, or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. The linear response is investigated introducing the conjugated gauge fields as external sources within the functional path integral approach. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for equilibrium thermodynamics, namely mean-field theory and a beyond-mean-field theory, taking into account mesonic contributions. Response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation. We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation, showing that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used to reveal the quark mass gap and the Mott dissociation of mesons, respectively. Noting that the mesonic contributions are not taken into account in the random phase approximation, we also derive the response functions parallel to the beyond-mean-field theory. We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions: the Aslamazov-Lakin contribution, the self-energy or density-of-state contribution, and the Maki-Thompson contribution. Unlike the equilibrium case, in evaluating the fluctuation contributions, we need to carefully treat the linear terms in external sources and the induced perturbations. In the chiral symmetry breaking phase, we find an additional chiral order parameter induced contribution, which ensures that the temporal component of the response functions in the static and long-wavelength limit recovers the correct charge susceptibility defined using the equilibrium thermodynamic quantities. These contributions from mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover, where the mesonic degrees of freedom are still important.

Dynamical axions and gravitational waves

In this paper we explore the possibility of observable gravitational waves as a manifestation of the QCD axion dynamics. In particular, we focus on dynamical axion models which solve the strong CP problem, and include the confinement of a QCD-like gauge group at the TeV scale. We study the resulting chiral symmetry breaking phase transition for models with NF = 3 and NF = 4 light flavors using the linear sigma model. This model describes the scalar meson spectrum and its interactions, with the diagonal field φ as the order parameter. We find that the amplitude of the gravitational wave spectrum depends on the mass of the dynamical axion η′ via the ratio {m}_{eta^{prime }}/{m}_{varphi } . The resulting spectra may be observed at future mid-range gravitational wave experiments such as AION/MAGIS, DECIGO, and BBO. Moreover, the TeV states can be searched for at colliders and their quantum numbers characterized, providing a unique connection between axion physics, gravitational waves and collider searches.

Holographic magnetized chiral density wave**S. L. is supported by One Thousand Talent Program for Young Scholars and NSFC (11675274, 11735007), Y. B. is supported by the Fundamental Research Funds for the Central Universities (122050205032) and the NSFC (11705037)

We explore the end point of the helical instability in a finite density, finite magnetic field background discussed by Kharzeev and Yee. The nonlinear solution is obtained and identified with the (magnetized) chiral density wave phase in the literature. We find there are two branches of solutions, which match the two unstable modes found before. At large chemical potential and magnetic field, the magnetized chiral density wave can be thermodynamically preferred over the chirally symmetric phase and chiral symmetry breaking phase. Interestingly, we find an exotic state with vanishing chemical potential at large magnetic field. We also attempt to clarify the role of anomalous charge in the holographic model.

Dense baryon matter with isospin and chiral imbalance in the framework of a NJL4 model at large Nc : Duality between chiral symmetry breaking and charged pion condensation

In this paper the phase structure of dense quark matter has been investigated in the presence of baryon, isospin and chiral isospin chemical potentials in the framework of (3+1)-dimensional Nambu--Jona-Lasinio model with two quark flavors. It has been shown that in the large-$N_{c}$ limit ($N_{c}$ is the number of colors of quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one. The key conclusion of our studies is the fact that chiral isospin chemical potential generates charged pion condensation in dense quark matter with isotopic asymmetry.

Duality and Charged Pion Condensation in Chirally Asymmetric Dense Quark Matter in the Framework of an NJL2 Model

In this talk we present investigation of the phase structure of a (1+1)-dimensional quark model with four-quark interaction and in the presence of baryon ([Formula: see text]), isospin ([Formula: see text]) and chiral isospin ([Formula: see text]) chemical potentials. Spatially homogeneous and inhomogeneous (chiral density wave (for chiral condensate) and single wave (for charged pion condensate)) condensates are considered. It is established that in the large-[Formula: see text] limit ([Formula: see text] is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. The primary conclusion of this investigation is the fact that chiral isospin chemical potential generates charged pion condensation with non-zero baryon density in dense quark matter. Moreover, it is shown that inhomogeneous charged PC phase with nonzero baryon density is induced in the model by arbitrary small values of the chemical potential [Formula: see text] (for a rather large region of [Formula: see text] and [Formula: see text]).

Affinity of NJL2 and NJL4 model results on duality and pion condensation in chiral asymmetric dense quark matter

In this paper we investigate the phase structure of a (1+1) and (3+1)-dimensional quark model with four-quark interaction and in the presence of baryon (μB), isospin (μI) and chiral isospin (μI5) chemical potentials. It is shown that the chemical potential μI5 promotes the appearance of the charged PC phase with nonzero baryon density. Results of both models are qualitatively the same, this fact enhances one's confidence in the obtained predictions. It is established that in the large-Nc limit (Nc is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation one.

A new method for the beta function in the chiral symmetry broken phase

We describe a new method to determine non-perturbatively the beta function of a gauge theory using lattice simulations in the p-regime of the theory. This complements alternative measurements of the beta function working directly at zero fermion mass and bridges the gap between the weak coupling perturbative regime and the strong coupling regime relevant to the mass spectrum of the theory. We apply this method to SU(3) gauge theory with two fermion flavors in the 2-index symmetric (sextet) representation. We find that the beta function is small but non-zero at the renormalized coupling value g2 = 6.7, consistent with our previous independent investigation using simulations directly at zero fermion mass. The model continues to be a very interesting explicit realization of the near-conformal composite Higgs paradigm which could be relevant for Beyond Standard Model phenomenology.

Low temperature electroweak phase transition in the Standard Model with hidden scale invariance

We discuss a cosmological phase transition within the Standard Model which incorporates spontaneously broken scale invariance as a low-energy theory. In addition to the Standard Model fields, the minimal model involves a light dilaton, which acquires a large vacuum expectation value (VEV) through the mechanism of dimensional transmutation. Under the assumption of the cancellation of the vacuum energy, the dilaton develops a very small mass at 2-loop order. As a result, a flat direction is present in the classical dilaton-Higgs potential at zero temperature while the quantum potential admits two (almost) degenerate local minima with unbroken and broken electroweak symmetry. We found that the cosmological electroweak phase transition in this model can only be triggered by a QCD chiral symmetry breaking phase transition at low temperatures, T≲132 MeV. Furthermore, unlike the standard case, the universe settles into the chiral symmetry breaking vacuum via a first-order phase transition which gives rise to a stochastic gravitational background with a peak frequency ∼10−8 Hz as well as triggers the production of approximately solar mass primordial black holes. The observation of these signatures of cosmological phase transitions together with the detection of a light dilaton would provide a strong hint of the fundamental role of scale invariance in particle physics.

Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of a NJL2 model

In this paper we investigate the phase structure of a ($1+1$)-dimensional quark model with four-quark interaction and in the presence of baryon (${\ensuremath{\mu}}_{B}$), isospin (${\ensuremath{\mu}}_{I}$), and chiral isospin (${\ensuremath{\mu}}_{I5}$) chemical potentials. Spatially inhomogeneous chiral density wave (for chiral condensate) and single wave (for charged pion condensate) approaches are used. It is established that in the large-${N}_{c}$ limit (${N}_{c}$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. Moreover, it is shown that inhomogeneous charged PC phase with nonzero baryon density is induced in the model by arbitrary small values of the chemical potential ${\ensuremath{\mu}}_{I5}$ (for a rather large region of ${\ensuremath{\mu}}_{B}$ and ${\ensuremath{\mu}}_{I}$).

Duality between chiral symmetry breaking and charged pion condensation at large Nc : Consideration of an NJL2 model with baryon, isospin, and chiral isospin chemical potentials

In this paper we investigate the phase structure of a (1+1)-dimensional schematic quark model with four-quark interaction and in the presence of baryon ($\mu_B$), isospin ($\mu_I$) and chiral isospin ($\mu_{I5}$) chemical potentials. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential $\mu_{I5}$ promotes the appearance of the charged PC phase with nonzero baryon density.

Phase transitions for SU(N) gauge theories with arbitrary number of flavors

We study the phase diagram of an [Formula: see text] gauge theory in terms of the number of colors [Formula: see text] and flavors [Formula: see text] with emphasis on the confinement and chiral symmetry breaking phases. We argue that as opposed to SUSY QCD there is a small region in the [Formula: see text] plane where the theory has the chiral symmetry broken but it is unconfined. The possibility of a new phase with strong confinement and chiral symmetry breaking is suggested.

Quantum and stringy corrections to the equation of state of holographic QCD matter and the nature of the chiral transition

We consider the finite temperature phase diagram of holographic QCD in the Veneziano limit (Nc large, Nf large with xf=Nf/Nc fixed) and calculate one string-loop corrections to the free energy in certain approximations. Such corrections, especially due to the pion modes are unsuppressed in the Veneziano limit. We find that under some extra assumptions the first order transition following from classical gravity solutions can become second order. If stringy asymptotics are of a special form and there are residual interactions it may even become of third order. Operationally these computations imply modelling the low temperature chiral symmetry breaking phase with a hadron gas containing Nf^2 massless Goldstone bosons and an exponential spectrum of massive hadrons. A third order transition is possible only if repulsive hadron interactions via the excluded volume effect are included.