$J/\Psi$ and ${\eta }_c$ above the QCD critical temperature $T_c$ are studied in anisotropic quenched lattice QCD, considering whether the $c\overline{c}$ systems above $T_c$ are spatially compact (quasi-)bound states or scattering states. We adopt the standard Wilson gauge action and $O(a)$-improved Wilson quark action with renormalized anisotropy $a_s/a_t=4.0$ at $\beta =6.10$ on ${16}^3\times (14–26)$ lattices, which correspond to the spatial lattice volume $V\equiv L^3\simeq (1.55\mathrm{fm}{)}^3$ and temperatures $T\simeq (1.11–2.07)T_c$. We investigate the $c\overline{c}$ system above $T_c$ from the temporal correlators with spatially extended operators, where the overlap with the ground state is enhanced. To clarify whether compact charmonia survive in the deconfinement phase, we investigate spatial boundary-condition dependence of the energy of $c\overline{c}$ systems above $T_c$. In fact, for low-lying $S$-wave $c\overline{c}$ scattering states, it is expected that there appears a significant energy difference $\Delta E\equiv E(\mathrm{APBC})-E(\mathrm{PBC})\simeq 2\sqrt{m_c^2+3{\pi }^2/L^2}-2m_c$ ($m_c$: charm quark mass) between periodic and antiperiodic boundary conditions on the finite-volume lattice. In contrast, for compact charmonia, there is no significant energy difference between periodic and antiperiodic boundary conditions. As a lattice QCD result, almost no spatial boundary-condition dependence is observed for the energy of the $c\overline{c}$ system in $J/\Psi$ and ${\eta }_c$ channels for $T\simeq (1.11–2.07)T_c$. This fact indicates that $J/\Psi$ and ${\eta }_c$ would survive as spatially compact $c\overline{c}$ (quasi-)bound states below $2T_c$. We also investigate a $P$-wave channel at high temperature with maximal entropy method and find no low-lying peak structure corresponding to ${\chi }_{c1}$ at $1.62T_c$.

We construct new solutions of the vacuum Einstein field equations in four dimensions via a solution-generating method utilizing the $\mathrm{SL}(2,R)$ symmetry of the reduced Lagrangian. We apply the method to an accelerating version of the Zipoy-Voorhees solution and generate new solutions which we interpret to be the accelerating versions of the Zipoy-Voorhees generalization of the Taub-NUT solution (with Lorentzian signature) and the Zipoy-Voorhees generalization of the Eguchi-Hanson solitons (with Euclidean signature). As an intermediary in the solution-generating process we obtain charged versions of the accelerated Zipoy-Voorhees-like families of solutions. Finally we present the accelerating version of the Taub-NUT solution and discuss its properties.

We probe the time dependence of the dark energy equation of state (EOS) in light of three-year WMAP (WMAP3) and the combination with other tentative cosmological observations from galaxy clustering (SDSS) and Type Ia Supernova (SNIa). We mainly focus on cases where the EOS is oscillating or with local bumps. By performing a global analysis with the Markov Chain Monte Carlo (MCMC) method, we find the current observations, in particular, the WMAP3 $+$ SDSS data combination, allow large oscillations of the EOS which can leave oscillating features on the (residual) Hubble diagram, and such oscillations are potentially detectable by future observations like SNAP, or even by the currently ongoing SNIa observations. Local bumps of dark energy EOS can also leave imprints on CMB, LSS and SNIa. In cases where the bumps take place at low redshifts and the effective EOS is close to $-1$, CMB and LSS observations cannot give stringent constraints on such possibilities. However, geometrical observations like (future) SNIa can possibly detect such features. On the other hand when the local bumps take place at higher redshifts beyond the detectability of SNIa, future precise observations like Gamma-ray bursts, CMB and LSS may possibly detect such features. In particular, we find that bumplike dark energy EOS on high redshifts might be responsible for the localized features of WMAP on ranges $l\sim 20-40$, which is interesting and deserves addressing further.

We investigate the laws of thermodynamics in an accelerating universe driven by dark energy with a time-dependent equation of state. In the case we consider that the physically relevant part of the Universe is that enveloped by the dynamical apparent horizon, we have shown that both the first law and second law of thermodynamics are satisfied. On the other hand, if the boundary of the Universe is considered to be the cosmological event horizon the thermodynamical description based on the definitions of boundary entropy and temperature breaks down. No parameter redefinition can rescue the thermodynamics laws from such a fate, rendering the cosmological event horizon unphysical from the point of view of the laws of thermodynamics.

We propose the generally covariant action for the theory of a self-coupled complex scalar field and electromagnetism which by virtue of constraints is equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics (MHD). We recover from it the Euler equation with Lorentz force, and the thermodynamic relations for a prefect fluid. The equation of state of the latter is related to the scalar field’s self potential. We introduce $1+3$ notation to elucidate the relation between MHD and field variables. In our approach the requirement that the scalar field be single valued leads to the quantization of a certain circulation in steps of $\hslash$; this feature leads, in the classical limit, to the conservation of that circulation. The circulation is identical to that in Oron’s generalization of Kelvin’s circulation theorem to perfect MHD; we here characterize the new conserved helicity associated with it. We also demonstrate the existence for MHD of two Bernoulli-like theorems for each spacetime symmetry of the flow and geometry; one of these is pertinent to suitably defined potential flow. We exhibit the conserved quantities explicitly in the case that two symmetries are simultaneously present, and give examples. Also in this case we exhibit a new conserved MHD circulation distinct from Oron’s, and provide an example.

A strong variable gravitational field of the very early Universe inevitably generates relic gravitational waves by amplifying their zero-point quantum oscillations. We begin our discussion by contrasting the concepts of relic gravitational waves and inflationary “tensor modes”. We explain and summarize the properties of relic gravitational waves that are needed to derive their effects on cosmic microwave background (CMB) temperature and polarization anisotropies. The radiation field is characterized by four invariants $I$, $V$, $E$, $B$. We reduce the radiative transfer equations to a single integral equation of Voltairre type and solve it analytically and numerically. We formulate the correlation functions $C_{\ell }^{X{X}^{\prime }}$ for $X$, $X^{\prime }=T$, $E$, $B$ and derive their amplitudes, shapes and oscillatory features. Although all of our main conclusions are supported by exact numerical calculations, we obtain them, in effect, analytically by developing and using accurate approximations. We show that the $TE$ correlation at lower $\ell$’s must be negative (i.e. an anticorrelation), if it is caused by gravitational waves, and positive if it is caused by density perturbations. This difference in $TE$ correlation may be a signature more valuable observationally than the lack or presence of the $BB$ correlation, since the $TE$ signal is about 100 times stronger than the expected $BB$ signal. We discuss the detection by WMAP of the $TE$ anticorrelation at $\ell \approx 30$ and show that such an anticorrelation is possible only in the presence of a significant amount of relic gravitational waves (within the framework of all other common assumptions). We propose models containing considerable amounts of relic gravitational waves that are consistent with the measured $TT$, $TE$ and $EE$ correlations.

Satellite galaxies currently undergoing tidal disruption offer a unique opportunity to constrain an effective violation of the equivalence principle in the dark sector. While dark matter in the standard scenario interacts solely through gravity on large scales, a new long-range force between dark-matter particles may naturally arise in theories in which the dark matter couples to a light scalar field. An inverse-square-law force of this kind would manifest itself as a violation of the equivalence principle in the dynamics of dark matter compared to baryons in the form of gas or stars. In a previous paper, we showed that an attractive force would displace stars outwards from the bottom of the satellite’s gravitational potential well, leading to a higher fraction of stars being disrupted from the tidal bulge further from the Galactic center. Since stars disrupted from the far (near) side of the satellite go on to form the trailing (leading) tidal stream, an attractive dark-matter force will produce a relative enhancement of the trailing stream compared to the leading stream. This distinctive signature of a dark-matter force might be detected through detailed observations of the tidal tails of a disrupting satellite, such as those recently performed by the Two-Micron All-Sky Survey (2MASS) and Sloan Digital Sky Survey (SDSS) on the Sagittarius (Sgr) dwarf galaxy. Here we show that this signature is robust to changes in our models for both the satellite and Milky Way, suggesting that we might hope to search for a dark-matter force in the tidal features of other recently discovered satellite galaxies in addition to the Sgr dwarf.

Measurement of the Yukawa interaction between the top quark and the Higgs boson should be useful to clarify the mechanism of fermion mass generation. We discuss the impact of nonstandard interactions characterized by dimension-six operators on the effective top Yukawa coupling. The cross section of the process $e^{-}{e}^{+}\to W^{-}{W}^{+}\nu \overline{\nu }\to t\overline{t}\nu \overline{\nu }$ is calculated including these operators, and possible deviation from the standard model prediction is evaluated under the constraint from perturbative unitarity and current experimental data. We find that if the new physics scale is in a TeV region, the cross section can be significantly enhanced due to the nonstandard interactions. Such a large effect should be detectable at the International Linear Collider.

Matter fields in the minimal supersymmetric standard model are chiral supermultiplets in fundamental (or singlet) representations of the standard model gauge group. In this paper we introduce chiral superfields in the adjoint representation of $SU(3{)}_C$ and study the effective field theory and phenomenology of them. These states are well motivated by intersecting D-brane models in which additional massless adjoint chiral supermultiplets appear generically in the low-energy spectrum. Although it has been pointed out that the existence of these additional fields may make it difficult to obtain asymptotic freedom, we demonstrate that this consideration does not rule out the existence of adjoints. The QCD gauge coupling can be perturbative up to a sufficiently high scale, and therefore a perturbative description for a D-brane model is valid. The full supersymmetric and soft SUSY breaking Lagrangians and the resulting renormalization group equations are given. Phenomenological aspects of the adjoint matter are also studied, including the decay and production processes. The similarity in gauge interaction between the adjoint fermion and gluino facilitates our study on these aspects. It is found that these adjoint multiplets can give detectable signals at colliders and satisfy the constraints from cosmology.

At the partonic level, a typical final state in small-$x$ deep inelastic scattering off nuclei and hard proton-nucleus collisions can be characterized by the multiplicity of color-excited nucleons. Within the Reggeon field theory, each color-excited nucleon is associated with the unitarity cut of the Pomeron exchanged between the projectile and nucleus. In this communication we derive the unitarity rules for the multiplicity of excited nucleons, alias cut pomerons, alias topological cross sections, for typical hard dijet production processes. We demonstrate how the coupled-channel non-Abelian intranuclear evolution of color dipoles, inherent to pQCD, gives rise to the Reggeon field theory diagrams for final states in terms of the uncut, and two kinds of cut, Pomerons. Upon the proper identification of the uncut and cut-Pomeron exchanges, the topological cross sections for dijet production follow in a straightforward way from the earlier derived nonlinear $k_{\perp }$ factorization quadratures for the inclusive dijet cross sections. The concept of a coherent (collective) nuclear glue proves extremely useful for the formulation of the Reggeon field theory vertices of multi-Pomeron—cut and uncut—couplings to particles and between themselves. A departure of our unitarity cutting rules from the ones suggested by the pre-QCD Abramovsky-Kancheli-Gribov rules, stems from the coupled-channel features of non-Abelian intranuclear pQCD. We propose a multiplicity resummation as a tool for the isolation of topological cross sections for single-jet production.

We are proposing a new way of describing families of quarks and leptons, using the approach unifying all the internal degrees of freedom, proposed by one of us [N. Mankoč Borštnik, Phys. Lett. B 292, 25 (1992).][N. Mankoč-Borštnik, J. Math. Phys. (N.Y.) 34, 3731 (1993).][N. Mankoč Borštnik, J. Math. Phys. (N.Y.) 36, 1593 (1995).][N. S. Mankoč Borštnik, Mod. Phys. Lett. A 10, 587 (1995).][N. S. Mankoč Borštnik and S. Fajfer, Nuovo Cimento Soc. Ital. Fis. B 112, 1637 (1997).][A. Borštnik and N. S. Mankoč Borštnik, in Proceedings to the International Workshop on “What Comes Beyond the Standard Model, Bled, Slovenia, 1998, edited by N. Mankoč Borštnik, H. B. Nielsen, and C. Froggatt (DMFA, Založništvo, 1999), p. 52.][N. S. Mankoč Borštnik and H. B. Nielsen, Phys. Rev. 62, 04010 (2000).][N. S. Mankoč Borštnik, Int. J. Theor. Phys. 40, 315 (2001), and references therein.][A. Borštnik and N. S. Mankoč Borštnik, in Proceedings to the International Workshop on “What Comes Beyond the Standard Model”, Bled 2000, 2001, 2002 Volume 2, edited by N. Mankoč Borštnik, H. B. Nielsen, C. Froggatt, and D. Lukman (DMFA, Založništvo, 2002), p. 27 and the paper (unpublished).][A. Borštnik and N. S. Mankoč Borštnik, in Proceedings to the Euroconference on Symmetries Beyond the Standard Model, Portorož, 2003 edited by N. Mankoč Borštnik, H. B. Nielsen, C. Froggatt, and D. Lukman (DMFA, Založništvo, 2003), pp. 27–51.]. Spinors, living in $d(=1+13)$-dimensional space, carry in this approach only the spin and interact with only the gravity through vielbeins and two kinds of the spin connection fields—the gauge fields of the Poincaré group $(p^a,S^{ab})$ and the second kind of the Clifford algebra objects (${\tilde{S}}^{ab}$). All the quarks and the leptons of one family appear in one Weyl representation of a chosen handedness of the Lorentz group, if analyzed with respect to the standard model gauge groups, which are subgroups of the group $SO(1,13)$: the right handed (with respect to $SO(1,3)$) weak chargeless quarks and leptons and the left handed weak charged quarks and leptons (with the right handed neutrino included). A part of the starting Lagrange density of a Weyl spinor in $d=1+13$ transforms right handed quarks and leptons into left handed quarks and leptons manifesting as the Yukawa couplings of the standard model. A kind of the Clifford algebra objects generates families of quarks and leptons and contributes to diagonal and off-diagonal Yukawa couplings. The approach predicts an even number of families, treating leptons and quarks equivalently (we do not study a possible appearance of Majorana fermions yet). In this paper we investigate within this approach the appearance of the Yukawa couplings within one family of quarks and leptons as well as among the families (without assuming any Higgs fields like in the standard model). We present the mass matrices for four families and investigate whether our way of generating families might explain the origin of families of quarks and leptons as well as their observed properties—the masses and the mixing matrices. Numerical results are presented in Ref. [M. Breskvar, D. Lukman, and N. S. Mankoč Borštnik, hep-ph/0606159.].

We develop a theory of static Bogomol’nyi-Prasad-Sommerfield (BPS) domain walls in stringy landscape and present a large family of BPS walls interpolating between different supersymmetric vacua. Examples include Kachru, Kallosh, Linde, Trivedi models, STU models, type IIB multiple flux vacua, and models with several Minkowski and anti-de Sitter vacua. After the uplifting, some of the vacua become de Sitter (dS), whereas some others remain anti-de Sitter. The near-BPS walls separating these vacua may be seen as bubble walls in the theory of vacuum decay. As an outcome of our investigation of the BPS walls, we found that the decay rate of dS vacua to a collapsing space with a negative vacuum energy can be quite large. The parts of space that experience a decay to a collapsing space, or to a Minkowski vacuum, never return back to dS space. The channels of irreversible vacuum decay serve as sinks for the probability flow. The existence of such sinks is a distinguishing feature of the landscape. We show that it strongly affects the probability distributions in string cosmology.

We extend the ordinary 3D electromagnetic duality to the noncommutative (NC) space-time through a Seiberg-Witten map to second order in the noncommutativity parameter $\theta$, defining a new scalar field model. There are similarities with the 4D NC duality; these are exploited to clarify properties of both cases. Up to second order in $\theta$, we find that duality interchanges the 2-form $\theta$ with its 1-form Hodge dual ${}^{\star }\theta$ times the gauge coupling constant, i.e., $\theta \to {}^{\star }\theta g^2$ (similar to the 4D NC electromagnetic duality). We directly prove that this property is false in the third order expansion in both 3D and 4D space-times, unless the slowly varying fields limit is imposed. Outside this limit, starting from the third order expansion, $\theta$ cannot be rescaled to attain an $S$-duality. In addition to possible applications on effective models, the 3D space-time is useful for studying general properties of NC theories. In particular, in this dimension, we deduce an expression that significantly simplifies the Seiberg-Witten mapped Lagrangian to all orders in $\theta$.

We confront the predictions of different quintessence models with recent measurements of the luminosity distance from two sets of supernovae type Ia. In particular, we consider the 157 SNe Ia in the Gold dataset with $z<1.7$, and the more recent data containing 71 supernovae obtained by the Supernova Legacy Survey (SNLS) with $z<1$. We numerically solve the evolution equations for the Ratra-Peebles inverse power-law model, the double exponential and the hyperbolic cosine quintessence models. We obtain confidence regions from the two datasets in the ${\Omega }_M-\alpha$ and ${\Omega }_M-w_{\varphi }$ planes for the different models and compare their predictions with dark energy models with constant equation of state.

It is shown that an effective (nonrenormalizable) coupling of lepton multiplets to scalar triplets in the 331 model with sterile/exotic neutrinos, can be a good way for generating neutrino masses of different types. The method is simple and avoids radiative/loop calculations which, sometimes, are long and complicated. Basing on some astrophysical arguments it is also stated that the scale of $SU(3{)}_L$ symmetry breaking is at TeV scale, in agreement with earlier investigations. Or equivalently, starting from this symmetry breaking scale we could have sterile/exotic neutrinos with mass of a few keV’s which could be used to explain several astrophysical and cosmological puzzles, such as the dark matter, the fast motion of the observed pulsars, the re-ionization of the Universe, etc.

We systematically apply density functional theory to determine the kind of inhomogeneities that spontaneously develop in a homogeneous gapless phase of neutral two-flavor superfluid quark matter. We consider inhomogeneities in the quark and electron densities and in the phases and amplitude of the order parameter. These inhomogeneities are expected to lead the gapless phase to a BCS-normal coexisting phase, a Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state with phase oscillations alone, and a LOFF state with amplitude oscillations. Using a simple model for the energy density functional, we find that which of them the homogeneous system tends towards depends sensitively on the chemical potential separation between up and down quarks and the gradient energies.

Maximal ’t Hooft loops are studied in $SO(3)$ lattice gauge theory at finite-temperature $T$. Tunneling barriers among twist sectors causing loss of ergodicity for local update algorithms are overcome through parallel tempering, enabling us to measure the vortex free energy $F$ and to identify a deconfinement transition at some ${\beta }_A^{\mathrm{crit}}$. The behavior of $F$ below ${\beta }_A^{\mathrm{crit}}$ shows however striking differences with what is expected from discretizations in the fundamental representation.

Five-dimensional Gauss-Bonnet gravity, with one warped extra-dimension, allows classes of solutions where two scalar fields combine either in a kink-antikink system or in a trapping-bag configuration. While the kink-antikink system can be interpreted as a pair of gravitating domain walls with opposite topological charges, the trapping-bag solution consists of a domain wall supplemented by a nontopological defect. In both classes of solutions, for large absolute values of the bulk coordinate (i.e. far from the core of the defects), the geometry is given by five-dimensional anti–de Sitter space.

We develop a general program of the unification of a matter-dominated era with an acceleration epoch for scalar-tensor theory or a dark fluid. The general reconstruction of the scalar-tensor theory is fulfilled. The explicit form of the scalar potential for which the theory admits a matter-dominated era, a transition to an acceleration, and an (asymptotically de Sitter) acceleration epoch consistent with Wilkinson Microwave Anisotropy Probe data is found. The interrelation of the epochs of deceleration-acceleration transition and matter dominance-dark energy transition for dark fluids with a general equation of state (EOS) is investigated. We give several examples of such models with explicit EOS (using redshift parametrization) where matter-dark energy domination transition may precede the deceleration-acceleration transition. As a by-product, the reconstruction scheme is applied to scalar-tensor theory to define the scalar potentials which may produce the dark matter effect. The obtained modification of Newton potential may explain the rotation curves of galaxies.