Mesons and diquarks in a color superconducting regime

The behavior of the mesons and diquarks is studied at finite temperatures, chemical potentials and densities, notably when the color superconductivity is taken into account. The Nambu and Jona-Lasinio model complemented by a Polyakov loop (PNJL description) has been adapted in order to model them in this regime. This paper focuses on the scalar and pseudoscalar mesons and diquarks, in a three-flavor and three-color description, with the isospin symmetry and at zero strange density. An objective of this work is to underline the modifications carried out by the color superconducting regime on the used equations and on the obtained results. It has been observed that the two-flavor color-superconducting (2SC) phase affects the masses and the coupling constants of the mesons and diquarks in a non-negligible way. This observation is particularly true at high densities and low temperatures for the pions, [Formula: see text] and the diquarks [Formula: see text] whose color is [Formula: see text]. This reveals that the inclusion of the color superconductivity in the modeling is relevant to describe the mesons and diquarks near the first-order chiral phase transition.

Correlations and Critical Behavior in Lattice Gluodynamics

In the Landau-gauge lattice gluodynamics we find that, both in the SU(2) and SU(3) theory, a correlation of the Polyakov loop with the asymmetry of the A2 gluon condensate as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We discuss finitevolume corrections and reveal that they can be reduced by the use of regression analysis. We also analyze the temperature dependence of low-momenta propagators in different Polyakov-loop sectors.

Monopoles of the Dirac type and color confinement in QCD

We present results of SU(3) Monte-Carlo studies of a new color confinement scheme proposed recently due to Abelian-like monopoles of the Dirac type corresponding in the continuum limit to violation of the non-Abelian Bianchi identities (VNABI). The simulations are done without any additional gauge-fixing smoothing the vacuum. We get for the first time, in pure SU(3) simulations, (1) the perfect Abelian dominance with respect to the static potentials on (12 ~ 16)4 at β = 5.6 − 5.8 using the multilevel method, (2) the monopole as well as Abelian dominances with respect to the static potentials by evaluating the Polyakov-loop correlators on 243 × 4 at β = 5.6. The Abelian photon part gives zero string tension. The new SU(3) as well as the previous SU(2) results are consistent with the new Abelian picture of color confinement that each one of eight colored electric flux is squeezed by the corresponding colored Abelian-like monopole of the Dirac type corresponding to VNABI.

Confinement-deconfinement transition and Z2 symmetry in Z2+Higgs theory

In this paper, we study the Polyakov loop and the [Formula: see text] symmetry in the lattice [Formula: see text] theory in four-dimensional space using Monte Carlo simulations. The results show that this symmetry is realized in the Higgs symmetric phase for large number of “temporal” lattice sites. To understand this dependence on the number of “temporal” sites, we consider a one-dimensional model by keeping terms of the original action corresponding to a single spatial site. In this approximation, the partition function can be calculated exactly as a function of the Polyakov loop. The resulting free energy is found to have the [Formula: see text] symmetry in the limit of large temporal sites. We argue that this is due to [Formula: see text] invariance as well as dominance of the distribution or density of states corresponding to the action.

Dark confinement-deconfinement phase transition: a roadmap from Polyakov loop models to gravitational waves

We explore the confinement-deconfinement phase transition (PT) of the first order (FO) arising in SU(N) pure Yang-Mills theory, based on Polyakov loop models (PLMs), in light of the induced gravitational wave (GW) spectra. We demonstrate that the PLMs with the Haar measure term, involving models successful in QCD with N = 3, are potentially incompatible with the large N scaling for the thermodynamic quantities and the latent heat at around the criticality of the FOPT reported from the lattice simulations. We then propose a couple of models of polynomial form, which we call the 4-6 PLM (with four- and six-point interactions among the basic PL fields which have center charge 1) and 4-8 PLM (with four- and eight-point interactions), and discuss how such models can naturally arise in the presence of a heavy PL with charge 2. We show that those models give the consistent thermodynamic and large N properties at around the criticality. The predicted GW spectra are shown to have high enough sensitivity to be probed in the future prospected interferometers such as BBO and DECIGO.

Color confinement and Bose-Einstein condensation

We propose a unified description of two important phenomena: color confinement in large-N gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the entropy from N0 to N2, which persists in the weak coupling region. Indistinguishability associated with the symmetry group — SU(N) or O(N) in gauge theory, and SN permutations in the system of identical bosons — is crucial for the formation of the condensed (confined) phase. We relate standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory. The constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter for the partially-(de)confined phase at finite coupling. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite N, and for quantum gravity via gauge/gravity duality.