We consider the phase diagram of QCD at very high baryon density and at zero temperature in the presence of a strong magnetic field. The state of matter at such high densities and low temperatures is believed to be a phase known as the color-flavor locked phase which breaks color and electromagnetic gauge invariance leaving a linear combination of them unbroken. Of the 9 quarks (three flavors and three colors), five are neutral under this unbroken generator and four are oppositely charged. In the presence of a magnetic field corresponding to the unbroken generator however, the properties of the condensate changes and a new phase known as the magnetic color flavor locked (MCFL)phase is realized. This phase breaks some of the color-flavor symmetry of the Lagrangian spontaneously, giving rise to 6 Goldstone modes, 5 of which are pseudo Goldstone modes. These Goldstone modes are composed of excitations that correspond to both neutral quarks and charged quarks. Hence it is natural to expect that the propagators of these Goldstone modes get affected in the presence of a magnetic field and their speed becomes considerably anisotropic. Although this anisotropy is self-evident from symmetry arguments, it has not been quantified yet. We calculate this anisotropy in the speed of the Goldstone modes using an NJL model type of interaction between the quarks and comment on the impact of such anisotropic modes on the transport properties of the MCFL phase.
The properties of the pseudoscalar Goldstone bosons in the color-flavor locked phase at moderate densities are studied within a model of the Nambu--Jona-Lasinio type. The Goldstone bosons are constructed explicitly by solving the Bethe-Salpeter equation for quark-quark scattering in random phase approximation. Main focus of our investigations are (i) the weak decay constant in the chiral limit, (ii) the masses of the flavored (pseudo-) Goldstone bosons for non-zero but equal quark masses, (iii) their masses and effective chemical potentials for non-equal quark masses, and (iv) the onset of kao…
The Bethe-Salpeter equations for diquarks with the quantum numbers of the Nambu-Goldstone bosons are analyzed in the color-flavor locked phase of cold dense QCD with three quark flavors. The decay constants and the velocities of the Nambu-Goldstone bosons are calculated in the Pagels-Stokar approximation. It is also shown that, in contrast to the case of dense QCD with two flavors, there are no massive radial excitations with quantum numbers of the Nambu-Goldstone bosons in the color-flavor locked phase. The role of the Meissner effect in the pairing dynamics of diquarks is explained.
A schematic NJL-type model is employed to investigate kaon and pion condensation in deconfined quark matter in the color-flavor locked (CFL) phase, explicitly referring to quark degrees of freedom. To that end we allow for non-vanishing pseudoscalar diquark condensates in addition to the scalar ones which constitute the CFL phase. Color neutrality is ensured by the appropriate choice of color chemical potentials. The dependence of the free energy in the Goldstone condensed phases on quark masses and charge chemical potentials is found to be in good qualitative -- in most cases also quantitativ…
The properties of pseudoscalar bosonic excitations in the color-flavor locked phase at moderate densities are studied within a model of the Nambu--Jona-Lasinio type. Our previous analysis is extended to Goldstone bosons with hidden flavor and to higher-lying modes which stay massive in the chiral limit. The bosons are constructed explicitly by solving the Bethe-Salpeter equation for quark-quark scattering in random phase approximation. The masses and weak decay constants of the Goldstone bosons are found in good agreement with predictions from the low-energy effective theory. In the non-Goldst…
We investigate the color-singlet order parameters and the quark description of the Nambu-Goldstone (NG) bosons in the color-flavor locked (CFL) phase. We put emphasis on the NG boson (phason) called ``H'' associated with the $\mathrm{U_B(1)}$ symmetry breaking. We qualitatively argue the nature of H as the second sound in the hydrodynamic regime. We articulate, based on a diquark picture, how the structural change of the condensates and the associated NG bosons occurs continuously from hadronic to CFL quark matter if the quark-hadron continuity is realized. We sharpen the qualitative differenc…
At very high densities, QCD is in the color-flavor locked phase, which is a color-superconducting phase. The diquark condensates break chiral symmetry in the same way as it is broken in vacuum QCD and gives rise to an octet of pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the charged and neutral kaons. For energies below the superconducting gap, the kaons are described by an $O(2)\times O(2)$-symmetric effective scalar field theory with chemical potentials. We use this effective theory to study Bose-condensation of kaons and their properties as functions of the tempe…
Inspired by the Goldstone equivalence gauge, we study the thermal corrections to an originally massive vector boson by checking the poles and branch cuts. We find that part of the Goldstone boson is spewed out from the longitudinal polarization, becoming a branch cut which can be approximated by the "quasi-poles" in the thermal environment. In this case, physical Goldstone boson somehow partly recovers. We also show the Feynmann rules for the "external legs" of these vector boson as well as the recovered Goldstone boson, expecting to simplify the vector boson participated process calculations …
A detailed analysis of collective modes that couple to either vector or axial color currents in color-flavor locked phase of color superconducting dense quark matter at finite temperature is presented. Among the realm of collective modes, including the plasmons and the Nambu-Goldstone bosons, we also reveal the gapless Carlson-Goldman modes, resembling the scalar Nambu-Golstone bosons. These latter exist only in a close vicinity of the critical line. Their presence does not eliminate the Meissner effect, proving that the system remains in the color broken phase. The finite temperature properti…
We study the low energy effective action for the collective modes of the color flavor locked phase of QCD. This phase of matter has long been known to be a superfluid because by picking a phase its order parameter breaks the quark-number $U(1)_B$ symmetry spontaneously. We consider the modes describing fluctuations in the magnitude of the condensate, namely the Higgs mode, and in the phase of the condensate, namely the Nambu-Goldstone (or Anderson-Bogoliubov) mode associated with the breaking of $U(1)_B$. By employing as microscopic theory the Nambu-Jona Lasinio model, we reproduce known resul…
The contribution of thermally excited electron-positron pairs to the bulk properties of the color-flavor locked quark phase inside compact stars is examined. The presence of these pairs causes the photon mean free path to be much smaller than a typical core radius ($R_0 \simeq 1$ km) for all temperatures above 25 keV so that the photon contribution to the thermal conductivity is much smaller than that of the Nambu-Goldstone bosons. We also find that the electrons and positrons dominate the electrical conductivity, while their contributions to the total thermal energy is negligible.
We study the behavior of Goldstone bosons in color-flavor-locked (CFL) quark matter at nonzero temperature. Chiral symmetry breaking in this phase of cold and dense matter gives rise to pseudo-Goldstone bosons, the lightest of these being the charged and neutral kaons K^+ and K^0. At zero temperature, Bose-Einstein condensation of the kaons occurs. Since all fermions are gapped, this kaon condensed CFL phase can, for energies below the fermionic energy gap, be described by an effective theory for the bosonic modes. We use this effective theory to investigate the melting of the condensate: we d…
Describing the lightest pseudoscalar mesons as bound states of quark and antiquark within the framework of an instantaneous Bethe-Salpeter formalism constructed such as to retain (in contrast to Salpeter's equation) as much information on the relativistic effects provided by the full quark propagator as conceivable allows for a surprisingly simple implementation of their near masslessness mandatory for their interpretability as pseudo-Goldstone bosons related to the spontaneous breaking of the chiral symmetries of quantum chromodynamics.
Quark matter at high density may exhibit color superconductivity. As magnetic flux tubes in metallic superconductors, color magnetic flux tubes as non-Abelian vortices appear in the color-flavor locked phase of high density QCD. ${\mathbb C}P^2$ Nambu-Goldstone bosons and Majorana fermions belonging to the triplet representation are known to be localized around a non-Abelian vortex. In this paper, we determine the coupling of these bosonic and fermionic modes by using the nonlinear realization method.
Enforcing color and electric charge neutrality conditions on the three-flavor color superconducting matter, I derive the explicit form of the quark propagators and the gluon self-energies for the gapless and the ordinary color-flavor-locked phases.
We discuss some low energy properties of color-flavor locked (CFL) superconductors. First, we study how an external magnetic field affects their Goldstone physics in the chiral limit, stressing that there is a long-range component of the field that penetrates the superconductor. We note that the most remarkable effect of the applied field is giving a mass to the charged pions and kaons. By estimating this effect, we see that for values $e B \sim 2 f_πΔ$, where $Δ$ is the quark gap, and $f_π$ the pion decay constant, the charged Goldstone bosons become so heavy, that they turn out to be unstabl…
The role of neutrality constraints for the phase structure of QCD at non-vanishing chemical potentials is studied within a self-consistent truncation scheme for the Dyson-Schwinger equation of the quark propagator in Landau gauge. We find the (approximate) color-flavor-locked phase to be energetically preferred at all potentially relevant densities and for physical values of the quark masses. We furthermore observe the impossibility to define this phase by residual global symmetries and discuss the role of chemical potentials.
Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavour-octet axial-vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD$^{N_c=2}$, where the colour singlet diquark is the ``baryon'' of the theory.
In this letter it is shown on general ground that there exist two qualitatively distinct solutions of the Dyson-Schwinger equation for the quark propagator in the case of non-zero current quark mass. One solution corresponds to the ``Nambu-Goldstone'' phase and the other one corresponds to the ``Wigner'' phase in the chiral limit.
We calculate the correlation functions needed to describe the linear response of superfluid matter, and go on to calculate the differential cross section for neutral-current neutrino scattering in superfluid neutron matter and in color-flavor locked quark matter (CFL). We report the first calculation of scattering rates that includes neutrino interactions with both pair-breaking excitations and low-lying collective excitations (Goldstone modes). Our results apply both above and below the critical temperature, allowing use in simulations of neutrino transport in supernovae and neutron stars.
In the presence of nonzero strange quark mass $m_s$, we investigate color neutrality in the $K^0$ condensed phase of color-flavor locked quark matter. By treating the $m_s$ effects on both kaon condensate and Fermi-surface phenomenon self-consistently, we develop a new treatment to evaluate color neutral solutions within the model-independent framework. It is pointed out that, in the general sense, the expectation values of gluon fields obtained from dynamics of Goldstone bosons solely are not identified with the factual color chemical potentials.
We study the transition of a scalar field in a fixed $AdS_{d+1}$ background between an extremum and a minimum of a potential. We compute analytically the solution to the perturbation equation for the vev deformation case by generalizing the usual matching method to higher orders and find the propagator of the boundary theory operator defined through the AdS-CFT correspondence. We show that, contrary to what happens at the leading order of the matching method, the next-to-leading order presents a simple pole at $q^2=0$ in accordance with the Goldstone theorem applied to a spontaneously broken d…
Color-flavor locked (CFL) quark matter at high densities is a color superconductor, which spontaneously breaks baryon number and chiral symmetry. Its low-energy thermodynamic and transport properties are therefore dominated by the H (superfluid) boson, and the octet of pseudoscalar pseudo-Goldstone bosons of which the neutral kaon is the lightest. We study the CFL-K^0 phase, in which the stress induced by the strange quark mass causes the kaons to condense, and there is an additional ultra-light "K^0" Goldstone boson arising from the spontaneous breaking of isospin. We compute the bulk viscosi…
We study weak interactions involving Goldstone bosons in the neutral kaon condensed phase of color flavor locked quark matter. We calculate the rates for the dominant processes that contribute to the neutrino mean free p ath and to neutrino production. A light $K^+$ state, with a mass $\tilde{m}_{K^+} \propto (Δ/μ) (Δ/m_s)(m_d-m_u)$, where $μ$ and $Δ$ are the quark chemical potential and superconducting gap respectively, is shown to play an important role. We identify unique characteristics of weak interaction rates in this novel phase and discuss how they might influence neutrino emission in …
We study the weak interaction rates involving Goldstone bosons in the Color Flavor Locked (CFL) quark matter. Neutrino mean free path and the rate of energy loss due to neutrino emission in a thermal plasma of CFL pions and kaons is calculated. We find that in addition to neutrino scattering off thermal mesons, novel Cherenkov like processes wherein mesons are either emitted or absorbed contribute to the neutrino opacity. Lack of Lorentz invariance in the medium and loss of rotational invariance for processes involving mesons moving relative to the medium allow for novel processes such as $π^0…
We apply a description of bound states of fermion and antifermion by means of our approximation to the Bethe-Salpeter formalism that retains part of the information on relativistic effects provided by the full fermion propagator to the lightest pseudoscalar mesons. Therein, the pseudo-Goldstone nature of the latter quark-antiquark bound states is taken into account by appropriately formulated effective interactions. Scrutinizing the predictions of this bound-state approach for meson masses, decay constants and in-meson condensates by relying on a generalized Gell-Mann-Oakes-Renner relation sho…
If quarks and gluons are either gapped or confined in neutron stars (NSs), the most relevant light modes are Nambu-Goldstone (NG) modes. We study NG modes within a schematic quark model whose parameters at high density are constrained by the two-solar mass constraint. Our model has the color-flavor-locked phase at high density, with the effective couplings as strong as in hadron physics. We find that strong coupling effects make NG modes more massive than in weak coupling predictions, and would erase several phenomena caused by the stressed pairings in mismatched Fermi surfaces. For instance, …
QCD superconductors in the color-flavor-locked (CFL) phase sustain light Goldstone modes (that will be referred to as generalized pions) that can be described as pairs of particle and/or hole excitations around a gapped Fermi surface. In weak coupling and to leading logarithm accuracy, their form factor, mass and decay constant can be evaluated exactly. These modes are found to satisfy an axial-Ward-identity, constraining the mass of the Goldstone modes in the CFL phase.
We show that the color-flavor locked (CFL) phase of dense quark matter is unstable with respect to the formation of a Goldstone boson current in the vicinity of the point $m_s^2=2μΔ$. In this Goldstone boson current phase all components of the magnetic screening mass are real.
We calculate neutrino emissivities from the decay and scattering of Goldstone bosons in the color-flavor-locked (CFL) phase of quarks at high baryon density. Interactions in the CFL phase are described by an effective low-energy theory. For temperatures in the tens of keV range, relevant to the long-term cooling of neutron stars, the emissivities involving Goldstone bosons dominate over those involving quarks, because gaps in the CFL phase are $\sim 100$ MeV while the masses of Goldstone modes are on the order of 10 MeV. For the same reason, the specific heat of the CFL phase is also dominated…
Some years ago Gribov developed the so-called supercritical light quark confinement scenario. Based on physical arguments he conjectured a drastic change in the analytical properties of the quark propagator when the back-reaction of Goldstone bosons (pions) is considered. We investigate this scenario and provide numerical solutions for the quark propagator in the complex plane with and without the pion back-reaction. We find no evidence for the scenario Gribov advocated. As an aside we present a novel method to solve the quark Dyson-Schwinger equation in the complex plane and discuss new chara…
At very high densities, QCD is in the color-flavor-locked phase, which is a color-superconducting phase. The diquark condensates break chiral symmetry in the same way as it is broken in vacuum QCD and gives rise to an octet of pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the charged and neutral kaons. For energies below the superconducting gap, the kaons are described by an $O(2)\times O(2)$-symmetric effective scalar field theory with chemical potentials. We use this effective theory to study Bose-condensation of kaons and their properties as functions of the tempe…
The properties of plasmons, Nambu-Goldstone bosons and gapless Carlson-Goldman collective modes in color-flavor locked phase of color superconducting dense quark matter at finite temperature are reviewed. A possibility of a kaon condensation with an abnormal number of the NG bosons is also discussed.
We study the structure of mass terms in the effective theory for quasi-particles in QCD at high baryon density. To next-to-leading order in the $1/p_F$ expansion we find two types of mass terms, chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov…
We study the stability of the kaon condensed color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a non-zero Goldstone boson current. In the kaon condensed phase there is an electrically charged fermion which becomes gapless near μ_s^(1) \simeq 1.35Δand a neutral fermion which becomes gapless near μ_s^(2)\simeq 1.61Δ. Here, μ_s=m_s^2/(2p_F) is the shift in the Fermi energy due to the strange quark mass m_s and Δis the gap in the chiral limit. The transition to the gapless phase is continuous at μ_s^(1) and first order at μ_s^(2). We find that the magnetic scree…
The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fi…
We present preliminary results for the chiral behavior of charged pseudo-Goldstone-boson masses and decay constants. These are obtained in simulations with N_f=2+1 flavors of tree-level, O(a)-improved Wilson sea quarks. In these simulations, mesons are composed of either valence quarks discretized in the same way as the sea quarks (unitary simulations) or of overlap valence quarks (mixed-action simulations). We find that the chiral behavior of the pseudoscalar meson masses in the mixed-action calculations cannot be explained with continuum, partially-quenched chiral perturbation theory. We sho…
The thermal conductivity of the color-flavor locked phase of dense quark matter is calculated. The dominant contribution to the conductivity comes from photons and Nambu-Goldstone bosons associated with breaking of baryon number which are trapped in the quark core. Because of their very large mean free path the conductivity is also very large. The cooling of the quark core arises mostly from the heat flux across the surface of direct contact with the nuclear matter. As the thermal conductivity of the neighboring layer is also high, the whole interior of the star should be nearly isothermal. Ou…
The thermal conductivity of the color-flavor locked phase of dense quark matter is calculated. The dominant contribution to the conductivity comes from photons and Nambu-Goldstone bosons associated with the breaking of baryon number, both of which are trapped in the quark core. Because of their very large mean free path the conductivity is also very large. The cooling of the quark core arises mostly from the heat flux across the surface of direct contact with the nuclear matter. As the thermal conductivity of the neighboring layer is also high, the whole interior of the star should be nearly i…
Within our description of Goldstone-type pseudoscalar mesons as almost massless bound states of quark and antiquark by a three-dimensional bound-state equation of Bethe-Salpeter origin, taking into account the pointwise behaviour of the full light-quark propagators enables to characterize the effective interquark interactions more precisely than earlier studies exploiting just specific aspects.
For a massive gauge theory with Higgs mechanism in a physical gauge, the longitudinal polarization of gauge bosons can be naturally identified as mixture of the goldstone component and a remnant gauge component that vanishes at the limit of zero mass, making the goldstone equivalence manifest. In light of this observation, we re-examine the Feynman rules of massive gauge theory by treating gauge fields and their corresponding goldstone fields as single objects, writing them uniformly as 5-component "vector" fields. The gauge group is taken to be $SU(2)_L$ to preserve custodial symmetry. We fin…
We study the stability of the color-flavor locked (CFL) phase of dense quark matter with regard to the formation of a non-zero Goldstone boson current. We show that an instability appears in the vicinity of the point $μ_s=Δ$ which marks the appearance of gapless fermion modes in the CFL phase. Here, $μ_s=m_s^2/(2μ)$ is the shift in chemical potential due to the strange quark mass and $Δ$ is the gap in the chiral limit. We show that in the Goldstone boson current phase all components of the magnetic screening mass are real. In this work we do not take into account homogeneous kaon condensation.…
The spectrum of meson and diquark excitations of dense quark matter is considered in the framework of the Nambu -- Jona-Lasinio model with three types of massless quarks in the presense of a quark number chemical potential $μ$. We investigate the effective action of meson- and diquark fields both at sufficiently large values of $μ>μ_c\approx 330$ MeV, where the color--flavor locked (CFL) phase is realized, and in the chirally broken phase of quark matter ($μ<μ_c$). In the last case all nine pseudoscalar mesons are Nambu -- Goldstone (NG) bosons, whereas the mass of the scalar meson nonet is tw…
We investigate the critical scaling of the quark propagator of N_f=2 QCD close to the chiral phase transition at finite temperature. We argue that it is mandatory to take into account the back-reaction effects of pions and the sigma onto the quark to observe critical behavior beyond mean field. On condition of self-consistency of the quark Dyson-Schwinger equation we extract the scaling behavior for the quark propagator analytically. Crucial in this respect is the correct pion dispersion relation when the critical temperature is approached from below. Our results are consistent with the known …
The $U_A(1)$ problem of QCD is inevitably tied to the infrared behaviour of quarks and gluons with its most visible effect being the $η^\prime$ mass. A dimensional argument of Kogut and Susskind showed that the mixing of the pseudoscalar flavour-singlet mesons with gluons can provide a screening of the Goldstone pole in this channel if the full quark-quark interaction is strongly infrared singular as $\sim 1/k^4$. We investigate this idea using previously obtained results for the Landau gauge ghost and gluon propagator, together with recent determinations for the singular behaviour of the quar…
We predict the existence of the gapless Carlson-Goldman modes in the color-flavor locked color superconducting phase of dense QCD. These modes resemble Nambu-Goldstone modes of the superconducting phase below the critical temperature where the Anderson-Higgs mechanism takes place. These modes exist in the broken phase in the vicinity of the critical line. Their presence does not eliminate the Meissner effect. The effect of Landau damping on the width of the Carlson-Goldman modes is discussed.
We study the effective field theory for fermions in the color-flavor locked (CFL) phase of high density QCD. The effective theory contains a flavor nonet of baryons interacting with a nonet of pseudoscalar Goldstone bosons as well as a singlet scalar Goldstone boson. The theory is similar to chiral perturbation theory in the one-baryon sector. We explain how to incorporate quark mass terms and study the spectrum as a function of the strange quark mass. Without meson condensation gapless baryon modes appears if the strange quark mass exceeds a critical value m_s^2/(2p_F)=Delta, where p_F is the…
We investigate spontaneous symmetry breaking within the linear sigma model with the SU(2)xU(1) internal symmetry at finite chemical potential, which was suggested as a model for kaon condensation in the CFL phase of dense quark matter. One-loop corrections to the scalar field effective potential as well as its propagator are calculated. Particular attention is paid to the type-II Goldstone boson that appears in the Bose--Einstein condensed phase. Furthermore, we show that the type-I Goldstone boson -- the superfluid phonon -- is allowed to decay due to the nonlinearity of its dispersion relati…
The combined absence of physical realizations of the UA(1) symmetry possessed by the classical QCD action in the chiral limit, and of an isoscalar Goldstone boson associated with its spontaneous breakdown, has been dubbed the UA(1) problem. A formal resolution of this problem proposed by 't Hooft relies on instantons to provide a mass to the would-be Goldstone boson (eta '). An alternate scheme for the generation of an eta ' mass proposed by Kogut and Susskind derives from quark annihilation into gluons and a strong infrared singularity in the gluon propagator associated with confinement. We d…
For the investigation of back-reactions of composite mesons in the NJL model, a variational path-integral treatment is formulated which yields an effective action $\mathscr{A}_{\rm eff}[D_σ,D_π; S]$, depending on the propagators $D_σ$, $D_π$ of $σ-$ and $π-$mesons and on the full quark propagator $S$. The stationarity conditions $δ\mathscr{A}_{\rm eff}/ δS = 0$, $δ\mathscr{A}_{\rm eff}/ δD_σ= 0$, $δ\mathscr{A}_{\rm eff}/ δD_π= 0$, then lead to coupled Schwinger-Dyson (SD) equations for the quark self-energy and the meson polarization functions. These results reproduce and extend results of the…
The role of the strange quark mass for the phase structure of QCD at non-vanishing densities is studied by employing a recently developed self-consistent truncation scheme for the Dyson-Schwinger equations of the quark propagators in Landau gauge. Hereby the medium modification of the effective quark interaction by the polarization of gluons is implemented. Taking into account this effect results in significantly smaller dynamical quark masses at the Fermi surface. Due to this reduction the color-flavor locked phase is always the preferred color-superconducting phase at zero temperature and fo…
Color superconductivity is expected to be formed in high density quark matter where color symmetry is spontaneously broken in the presence of di-quark condensate. Stable non-Abelian vortices or color magnetic flux tubes exist in the color-flavor locked phase at asymptotically high density. $\mathbb{C}P^2$ Nambu-Goldstone(NG) bosons and Majorana fermions belonging to the triplet representation are localized around a non-Abelian vortex. We discuss the zero mode analysis and the low-energy effective world sheet theory of a non-Abelian vortex. We determine the interactions of these bosonic and fer…
We investigate the color-spin locked (CSL) phase of spin-one color- superconducting quark matter using a truncated Dyson-Schwinger equation for the quark propagator in Landau gauge. Starting from the most general parity conserving ansatz allowed by the CSL symmetry, the Dyson-Schwinger equation is solved self-consistently and dispersion relations are discussed. We find that chiral symmetry is spontaneously broken due to terms which have previously been neglected. As a consequence, the excitation spectrum contains only gapped modes even for massless quarks. Moreover, at moderate chemical potent…
The spectrum of meson and diquark excitations of the color--flavor locked (CFL) phase of dense quark matter is considered in the framework of the Nambu -- Jona-Lasinio model. We have found that in this phase all Nambu--Goldstone bosons are realized as scalar and pseudoscalar diquarks. Other diquark excitations are resonances with mass value around 230 MeV. Mesons are stable particles in the CFL phase. Their masses vs chemical potential lie in the interval 300$÷$500 MeV.
We investigate collective excitations coupled with baryon density in a system of massless three-flavor quarks in the collisionless regime. By using the Nambu-Jona-Lasinio (NJL) model in the mean-field approximation, we derive the spectra both for the normal and color-flavor locked (CFL) superfluid phases at zero temperature. In the normal phase, we obtain zero sound as a low-lying collective mode in the particle-hole (vector) channel. In the CFL phase, when the excitation energy, $ω$, is smaller than the threshold given by twice the pairing gap $Δ$ ($ω<2Δ$), a phonon corresponding to fluctuati…
We propose a new non-Hermitian chiral random matrix model that describes single-flavor spin-one Cooper pairing of quarks. For three colors the model shows spontaneous breaking of color $\mathrm{SU}(3)_C$ and spin $\mathrm{SO}(3)_J$ symmetries down to the diagonal $\mathrm{SO}(3)_{C+J}$ subgroup, in striking analogy to the color-spin locked phase of one-flavor QCD at high density. For two colors, color-singlet spin-one diquarks condense and trigger symmetry breaking $\mathrm{U}(1) \times \mathrm{SO}(3)_J \to \mathrm{SO}(2)_J$. In both cases the microscopic large-$N$ limit is rigorously taken an…
Quark-hadron continuity is a scenario that hadronic matter is continuously connected to color superconductor without phase transitions as the baryon chemical potential increases. This scenario is based on Landau's classification of phases since they have the same symmetry breaking pattern. We address the question whether this continuity is true as quantum phases of matter, which requires the treatment beyond Ginzburg-Landau description. To examine the topological nature of color superconductor, we derive a dual effective theory for $U(1)$ Nambu-Goldstone (NG) bosons and vortices of the color-f…
A field model for a quark and an antiquark binding is described. Quarks interact via a gauge unparticle ("ungluons"). The model is formulated in terms of Lagrangian which features the source field $S(x)$ which becomes a local pseudo-Goldstone field of conformal symmetry - the pseudodilaton mode and from which the gauge non-primary unparticle field is derived by $B_μ(x) \sim\partial_μ S(x)$. Because the conformal sector is strongly coupled, the mode $S(x)$ may be one of new states accessible at high energies. We have carried out an analysis of the important quantity that enters in the "ungluon"…
At zero temperature and density, the nature of the chiral phase transition in QED$_3$ with $\textit{N}_{f}$ massless fermion flavors is investigated. To this end, in Landau gauge, we numerically solve the coupled Dyson-Schwinger equations for the fermion and boson propagator within the bare and simplified Ball-Chiu vertices separately. It is found that, in the bare vertex approximation, the system undergoes a high-order continuous phase transition from the Nambu-Goldstone phase into the Wigner phase when the number of fermion flavors $\textit{N}_{f}$ reaches the critical number $\textit{N}_{f,…
In QCD at high density, the color-octet quark-antiquark condensate $\langle\overlineψγ_0(λ^A)_C (λ^A)_Fψ\rangle$ is generally nonzero and dynamically breaks the $\mathrm{SU}(3)_C\times \mathrm{SU}(3)_L\times\mathrm{SU}(3)_R$ symmetry down to the diagonal $\mathrm{SU}(3)_V$. We evaluate this condensate in the mean-field approximation and find that it is of order $μΔ^2\log(μ/Δ)$ where $Δ$ is the BCS gap of quarks. Next we propose a novel non-Hermitian chiral random matrix theory that describes the formation of colorful quark-antiquark condensates. We take the microscopic large-$N$ limit and find…
