In this paper, we study two-color, two-flavor QCD using chiral perturbation theory at next-to-leading order when the diquark chemical potential ($μ_{B}$) is equal to the isospin chemical potential ($μ_{I}$). For chemical potentials larger than the physical pion mass, the system is in a multicomponent superfluid phase with both pions and diquarks. We construct the one-loop effective potential using $χ$PT in the presence of an external multicomponent superfluid source and use the effective potential to calculate the chiral condensate, the multicomponent superfluid condensate and the (multicomponent) superfluid density. We also find the critical chemical potential and the order of the phase transition from the normal phase to the multicomponent condensed phase at next-to-leading order. The phase transition remains second order (as at tree-level) and the critical chemical potential is equal to the one-loop renormalized diquark (or pion) mass.
We describe the interplay of two nonperturbative phenomena which should take place in the chirally invariant deconfined phase of QCD matter at finite density and T=0: (i) Cooper-pair quark-quark ground-state condensation in appropriate channels should yield exotic sorts of color superfluidity, and (ii) quark-antiquark ground-state condensation should yield spontaneous breakdown of chiral symmetry. We briefly review the main recent achievements in the subject, and present the field-theory formalism which enables to deal with both above mentioned types of condensates simultaneously.
The effects of chiral imbalance and external magnetic field on pion superfluidity and color superconductivity are investigated in extended Nambu--Jona-Lasinio models. We take Schwinger approach to treat the interaction between charged pion condensate and magnetic field at finite isospin density and include simultaneously the chiral imbalance and magnetic field at finite baryon density. For the superfluidity, the chiral imbalance and magnetic field lead to catalysis and inverse catalysis effects, respectively. For the superconductivity, the chiral imbalance enhances the critical baryon density,…
We discuss the phase structure of quantum chromodynamics (QCD) with two colors and two flavors of light quarks. This is motivated by the increasing interest in the QCD phase diagram as follows: (1) The QCD critical point search has been under intensive dispute and its location and existence suffer from uncertainty of effective U(1)_A symmetry restoration. (2) A new phase called quarkyonic matter is drawing theoretical and experimental attention but it is not clear whether it can coexist with diquark condensation. We point out that two-color QCD is nontrivial enough to contain essential ingredi…
I clarify how the concept of quark-hadron continuity, which was previously considered in the context of the asymptotic color-flavor locked phase with ideal three-flavor symmetry, is applied to two-flavor matter. Our observation is that neutron star matter can continuously be connected to two-flavor color-superconducting (2SC) phase with an additional condensate of $d$-quarks in the $^3P_2$ channel. I discuss here two aspects of this novel phase. First, I introduce the notion of continuity based on the patterns of symmetry breaking and the corresponding order parameters, and then explain qualit…
We propose a wide universality class of gapless superfluids, and analyze a limit that might be realized in quark matter at intermediate densities. In the breached pairing color superconducting phase heavy $s$-quarks, with a small Fermi surface, pair with light $u$ or $d$ quarks. The groundstate has a superfluid and a normal Fermi component simultaneously. We expect a second order phase transition, as a function of increasing density, from the breached pairing phase to the conventional color-flavor locked (CFL) phase.
Based upon the analogy to the electroweak phase diagram, I propose that in QCD there might be a critical line for a superfluid transition, in the plane of chemical potential and temperature. The order parameter has the quantum numbers of the H-dibaryon, but the transition is driven by color superconductivity in strange quark matter.
We investigate pion superfluidity in the frame of two flavor Nambu--Jona-Lasinio model beyond mean field approximation. We calculate the thermodynamics to the next to leading order in an expansion in the inverse number of colors, including both quark and meson contributions at finite temperature and baryon and isospin density. Due to the meson fluctuations, the Sarma phase which exists at mean field level is washed away, and the Bose-Einstein condensation region at low isospin density is highly suppressed.
We discuss the low-energy dynamics of superfluidity with topological order in $(3+1)$ spacetime dimensions. We generalize a topological $BF$ theory by introducing a non-square $K$ matrix, and this generalized $BF$ theory can describe massless Nambu-Goldstone bosons and anyonic statistics between vortices and quasiparticles. We discuss the general structure of discrete and continuous higher-form symmetries in this theory, which can be used to classify quantum phases. We describe how to identify the appearance of topological order in such systems and discuss its relation to a mixed 't Hooft anom…
Matter at intermediate baryon densities and low temperatures is notoriously hard to tackle theoretically. Whereas lattice methods cannot cover more than rather small densities, perturbative methods are only applicable at much higher densities. The regime of intermediate chemical potential at low temperatures in the QCD-phase diagram is therefore out of reach of first-principle methods, thus we have to rely on stellar objects to investigate dense nuclear and quark matter at low temperatures. Compact stars can serve as an unique laboratory for this regime. Due to their fast rotation and high mag…
We investigate pion superfluidity and its effect on meson properties and equation of state at finite temperature and isospin and baryon densities in the frame of standard flavor SU(2) NJL model. In mean field approximation to quarks and random phase approximation to mesons, the critical isospin chemical potential for pion superfluidity is exactly the pion mass in the vacuum, and corresponding to the isospin symmetry spontaneous breaking, there is in the pion superfluidity phase a Goldstone mode which is the linear combination of the normal sigma and charged pion modes. We calculate numerically…
Color magnetic flux tubes appear in the color-flavor locked phase of high density QCD, which exhibits color superconductivity as well as superfluidity. They are non-Abelian superfluid vortices and are accompanied by orientational zero modes in the internal space associated with the color-flavor locked symmetry spontaneously broken in the presence of the vortex. We show that those zero modes are localized around the vortex in spite of the logarithmic divergence of its tension, and derive the low-energy effective theory of them on the world-sheet of the vortex-string.
We describe the crystalline phase of color superconducting quark matter. This phase may occur in quark matter at densities relevant for compact star physics, with possible implications for glitch phenomena in pulsars. We use a Ginzburg-Landau approach to determine that the crystal has a face-centered-cubic (FCC) structure. Moreover, our results indicate that the phase is robust, with gaps, critical temperature, and free energy comparable to those of the color-flavor-locked (CFL) phase. Our calculations also predict ``crystalline superfluidity'' in ultracold gases of fermionic atoms.
Superfluidity or superconductivity with mismatched Fermi momenta appears in many systems such as charge neutral dense quark matter, asymmetric nuclear matter, and in imbalanced cold atomic gases. The mismatch plays the role of breaking the Cooper pairing, and the pair-breaking state cannot be properly described in the framework of standard BCS theory. I give a brief review on recent theoretical development in understanding unconventional color superconductivity, including gapless color superconductor, the chromomagnetic instabilities and the Higgs instability in the gapless phase. I also intro…
We study the bosonic excitations in the favorite cubic three flavor crystalline LOFF phases of QCD. We calculate in the Ginzburg-Landau approximation the masses of the eight pseudo Nambu-Goldstone Bosons (NGB) present in the low energy theory. We also compute the decay constants of the massless NGB Goldstones associated to superfluidity as well as those of the eight pseudo NGB. Differently from the corresponding situation in the Color-Flavor-Locking phase, we find that meson condensation phases are not expected in the present scenario.
The recent study by Bowers and Rajagopal on the possible structures for the QCD crystalline color superconducting phase favors a cubic structure and allows for a first discussion of the QCD dynamics in the crystalline phase. The cubic structure leads to complete breaking of traslation invariance and to three phonon modes. We discuss the expected form of the effective Lagrangian and the phonon dispersion laws assuming the proposed crystal structure. Besides the interest for QCD and the related possible relevance to compact stars these considerations may become useful to atomic systems exhibitin…
The hydrodynamic description of a superfluid is usually based on a two-fluid picture. We compute the basic properties of the relativistic two-fluid system from the underlying microscopic physics of a relativistic φ^4 complex scalar field theory. We work at nonzero but small temperature and weak coupling, and we neglect dissipation. We clarify the relationship between different formulations of the two-fluid model, and how they are parameterized in terms of partly redundant current and momentum 4-vectors. As an application, we compute the velocities of first and second sound at small temperature…
Quark-hadron continuity with two-flavor quarks that was proposed recently connects hadronic matter with neutron $^3P_2$ superfluidity and two-flavor dense quark matter. This two-flavor dense quark phase consists of the coexistence of the 2SC condensates and the $P$-wave diquark condensates of $d$-quarks, which gives rise to color superconductivity as well as superfluidity. We classify vortices in this phase. The most stable vortices are what we call the non-Abelian Alice strings, which are superfluid vortices with non-Abelian color magnetic fluxes therein, exhibiting so-called topological obst…
Neutrino energy losses through neutral weak currents in the triplet-spin superfluid neutron liquid are studied for the case of condensate involving several magnetic quantum numbers. Low-energy excitations of the multicomponent condensate in the timelike domain of the energy and momentum are analyzed. Along with the well-known excitations in the form of broken Cooper pairs, the theoretical analysis predicts the existence of collective waves of spin density at very low energy. Because of a rather small excitation energy of spin waves, their decay leads to a substantial neutrino emission at the l…
We find a novel confinement mechanism in the two-flavor dense quark matter proposed recently, that consists of the 2SC condensates and the $P$-wave diquark condensates of $d$-quarks. This quark matter exhibiting color superconductivity as well as superfluidity is classified into two phases; confined and deconfined phases of vortices. We establish that the criterion of the confinement is color neutrality of Aharonov-Bohm (AB) phases: vortices exhibiting color non-singlet AB phases are confined by the so-called AB defects to form color-singlet bound states. In the deconfined phase, the most stab…
We explore the phase structure of two-color and two-flavor QCD in the space of the quark chemical potential μ_q and the isospin chemical potential μ_I. Using a mean-field model we calculate the chiral and diquark condensates, σand Δ, self-consistently. In weak coupling and in the chiral limit, we confirm the interval of the isospin chemical potential, 0.71Δ_0<μ_I<0.75Δ_0, in which a single plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase is favored over isotropic superfluidity and normal quark matter. The LOFF window becomes slightly wider at high density. For stronger coupling with no…
We investigate the effects of pairing fluctuations in fermionic superfluids/superconductors where pairing occurs among three species (colors) of fermions. Such color superfluids/superconductors can be realized in three-component atomic Fermi gases and in dense quark matter. The superfluidity/superconductivity is characterized by a three-component order parameter which denotes the pairing among the three colors of fermions. Due to the SU$(3)$ symmetry of the Hamiltonian, one color does not participate pairing. This branch of fermionic excitation is gapless in the naive BCS mean-field descriptio…
The two-dimensional, massless Gross-Neveu model with Nc colors and SU(2) isospin is studied analytically in the large Nc limit. The chiral SU(2)L X SU(2)R symmetry is broken spontaneously in the vacuum. Twisted kinks connecting two arbitrary points on the vacuum manifold S3 are constructed, and their properties are explored. The phase diagram as a function of temperature, baryon- and isospin chemical potential is discussed, with special emphasis on inhomogeneous phases. The preferred form of the condensate is a product of the real kink crystal and the chiral spiral. Kink-kink scattering is sol…
We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high ch…
QCD-like theories possess a positively definite fermion determinant at finite baryon chemical potential $μ_{\text B}$ and the lattice simulation can be successfully performed. While the chiral perturbation theories are sufficient to describe the Bose condensate at low density, to describe the crossover from Bose-Einstein condensation (BEC) to BCS superfluidity at moderate density we should use some fermionic effective model of QCD, such as the Nambu-Jona-Lasinio model. In this paper, using two-color two-flavor QCD as an example, we examine how the Nambu-Jona-Lasinio model describes the weakly …
