We investigate the confining phase transition as a function of temperature for theories with dynamical fermions in the two index symmetric and antisymmetric representation of the gauge group. By studying the properties of the center of the gauge group we predict for an even number of colors a confining phase transition, if second order, to be in the universality class of Ising in three dimensions. This is due to the fact that the center group symmetry does not break completely for an even number of colors. For an odd number of colors the center group symmetry breaks completely. This pattern remains unaltered at a large number of colors. The confining/deconfining phase transition in these theories at large and finite $N$ is not mapped in the one of super Yang-Mills theory. We extend the Polyakov loop effective theory to describe the confining phase transition of the theories studied here for a generic number of colors. Our results are not modified when adding matter in the same higher dimensional representations of the gauge group. We comment on the interplay between confinement and chiral symmetry in these theories and suggest that they are ideal laboratories to shed light on this issue also for ordinary QCD. We compare the free energy as a function of temperature for different theories. We find that the conjectured thermal inequality between the infrared and ultraviolet degrees of freedom computed using the free energy does not lead to new constraints on asymptotically free theories with fermions in higher dimensional representations of the gauge group. Since the center of the gauge group is an important quantity for the confinement properties at zero temperature our results are relevant here as well.

We propose a generalization of the condition for harmonic spatial coordinates analogous to the generalization of the harmonic time slices introduced by Bona et al., and closely related to dynamic shift conditions recently proposed by Lindblom and Scheel, and Bona and Palenzuela. These generalized harmonic spatial coordinates imply a condition for the shift vector that has the form of an evolution equation for the shift components. We find that in order to decouple the slicing condition from the evolution equation for the shift it is necessary to use a rescaled shift vector. The initial form of the generalized harmonic shift condition is not spatially covariant, but we propose a simple way to make it fully covariant so that it can be used in coordinate systems other than Cartesian. We also analyze the effect of the shift condition proposed here on the hyperbolicity of the evolution equations of general relativity in $1+1$ dimensions and $3+1$ spherical symmetry, and study the possible development of blowups. Finally, we perform a series of numerical experiments to illustrate the behavior of this shift condition.

We study the structure of stationary and axisymmetric metrics solving the vacuum Einstein equations of general relativity in four and higher dimensions, building on recent work in Phys. Rev. D 70, 124002 (2004). We write the Einstein equations in a new form that naturally identifies the sources for such metrics. The sources live in a one-dimensional subspace and the entire metric is uniquely determined by them. We study in detail the structure of stationary and axisymmetric metrics in four dimensions, and consider as an example the sources of the Kerr black hole.

We describe the possibility of using the laser interferometer space antenna (LISA) ’s gravitational-wave observations to study, with high precision, the response of a massive central body (e.g. a black hole or a soliton star) to the tidal gravitational pull of an orbiting, compact, small-mass object (a white dwarf, neutron star, or small-mass black hole). Motivated by this LISA application, we use first-order perturbation theory to study tidal coupling for a special, idealized case: a Schwarzschild black hole of mass $M$, tidally perturbed by a “moon” with mass $\mu \ll M$ in a circular orbit at a radius $b\gg M$ with orbital angular velocity $\Omega$. We investigate the details of how the tidal deformation of the hole gives rise to an induced quadrupole moment ${\mathcal{I}}_{ij}$ in the hole’s external gravitational field at large radii, including the vicinity of the moon. In the limit that the moon is static, we find, in Schwarzschild coordinates and Regge-Wheeler gauge, the surprising result that there is no induced quadrupole moment. We show that this conclusion is gauge dependent and that the static, induced quadrupole moment for a black hole is inherently ambiguous, and we contrast this with an earlier result of Suen, which gave, in a very different gauge, a nonzero static induced quadrupole moment with a sign opposite to what one would get for a fluid central body. For the orbiting moon and the central Schwarzschild hole, we find (in agreement with a recent result of Poisson) a time-varying induced quadrupole moment that is proportional to the time derivative of the moon’s tidal field, ${\mathcal{I}}_{ij}=(32/45)M^6{\dot{\mathcal{E}}}_{ij}$ and that therefore is out of phase with the tidal field by a spatial angle $\pi /4$ and by a temporal phase shift $\pi /2$. This induced quadrupole moment produces a gravitational force on the moon that reduces its orbital energy and angular momentum at the same rate as the moon’s tidal field sends energy and angular momentum into the hole’s horizon. As a partial analog of a result derived long ago by Hartle for a spinning hole and a static distant companion, we show that the orbiting moon’s tidal field induces a tidal bulge on the hole’s horizon, and that the rate of change of the horizon shape (i.e. the horizon shear) leads the perturbing tidal field at the horizon by an angle $4M\Omega$. We prefer to avoid introducing an ingoing null geodesic, as Hartle did in his definition of the phase shift, because the moon is in the central body’s near zone ($b\ll 1/\Omega$) and thus should interact with the horizon instantaneously, not causally. We discuss the implications of these results for LISA’s future observations of tidal coupling, including the inappropriateness of using the concepts of tidal polarizability and tidal lag or lead angle, for the massive central body, when discussing LISA’s observations.

We study the general properties of a spherically symmetric body described through the generalized Chaplygin equation of state. We conclude that such an object, dubbed generalized Chaplygin dark star, should exist within the context of the generalized Chaplygin gas (GCG) model of unification of dark energy and dark matter, and derive expressions for its size and expansion velocity. A criteria for the survival of the perturbations in the GCG background that give origin to the dark star are developed, and its main features are analyzed.

We study the spectrum of gravitational perturbations about a vacuum de Sitter brane with the induced 4D Einstein-Hilbert term, in a 5D Minkowski spacetime (DGP model). We consider solutions that include a self-accelerating universe, where the accelerating expansion of the universe is realized without introducing a cosmological constant on the brane. The mass of the discrete mode for the spin-2 graviton is calculated for various $H{r}_c$, where $H$ is the Hubble parameter and $r_c$ is the crossover scale determined by the ratio between the 5D Newton constant and the 4D Newton constant. We show that, if we introduce a positive cosmological constant on the brane ($H{r}_c>1$), the spin-2 graviton has mass in the range $0<m^2<2H^2$ and there is a normalizable brane fluctuation mode with mass $m^2=2H^2$. Although the brane fluctuation mode is healthy, the spin-2 graviton has a helicity-0 excitation that is a ghost. If we allow a negative cosmological constant on the brane, the brane fluctuation mode becomes a ghost for $1/2<H{r}_c<1$. This confirms the results obtained by the boundary effective action that there exists a scalar ghost mode for $H{r}_c>1/2$. In a self-accelerating universe $H{r}_c=1$, the spin-2 graviton has mass $m^2=2H^2$, which coincides with the mass of the brane fluctuation mode. Then there arises a mixing between the brane fluctuation mode and the spin-2 graviton. We argue that this mixing presumably gives a ghost in the self-accelerating universe by continuity across $H{r}_c=1$, although a careful calculation of the effective action is required to verify this rigorously.

We present a calculation of neutrino pair bremsstrahlung due to electron-electron scattering in a relativistic degenerate plasma of electrons. Proper treatment of the in-medium photon propagator, i.e., inclusion of Debye screening of the longitudinal part and Landau damping of the transverse part, leads to a neutrino emissivity which is several orders of magnitude larger than when Debye screening is imposed for the tranverse part. Our results show that this in-medium process can compete with other sources of neutrino radiation and can, in some cases, even be the dominant neutrino emission mechanism. We also discuss the natural extension to quark-quark bremsstrahlung in gapped and ungapped quark matter.

We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black-hole formation.

For SU(2) lattice gauge theory with the fundamental-adjoint action an efficient heat-bath algorithm is not known so that one had to rely on Metropolis simulations supplemented by overrelaxation. Implementing a novel biased Metropolis-heat-bath algorithm for this model, we find improvement factors in the range 1.45 to 2.06 over conventionally optimized Metropolis simulations. If one optimizes further with respect to additional overrelaxation sweeps, the improvement factors are found in the range 1.3 to 1.8.

Because of its complex structure the parametrized fixed point action can not be simulated with the available local updating algorithms. We constructed, coded, and tested an updating procedure with $2+1$ light flavors, where the targeted $s$ quark mass is at its physical value while the $u$ and $d$ quarks should produce pions lighter than 300 MeV. In the algorithm a partially global gauge update is followed by several accept/reject steps, where parts of the determinant are switched on gradually in the order of their costs. The trial configuration that is offered in the last, most expensive, stochastic accept/reject step differs from the original configuration by a Metropolis $+$ over-relaxation gauge update over a subvolume of $\sim (1.3\mathrm{fm}{)}^4$. The acceptance rate in this accept/reject step is $\sim 0.4$. The code is optimized on different architectures and is running on lattices with $L_s\approx 1.2\mathrm{fm}$ and 1.8 fm at a resolution of $a\approx 0.15\mathrm{fm}$.

The mass of the $1^{-+}$ exotic meson, created with hybrid interpolating fields, is explored in numerical simulations of quenched QCD on large (${20}^3\times 40$) lattices to obtain good control of statistical and finite volume errors. Using the Fat-Link Irrelevant Clover (FLIC) fermion action, the properties of the $1^{-+}$ are investigated at light quark masses approaching 25 MeV ($m_{\pi }/m_{\rho }\simeq 1/3$). Under the standard assumption that the coupling to the quenched $a_1{\eta }^{\prime }$ channel comes with a negative metric, our results indicate that the $1^{-+}$ exotic exhibits significant curvature close to the chiral limit, suggesting previous linear extrapolations have overestimated the mass of the $1^{-+}$. We find for the first time in lattice studies a $1^{-+}$ mass consistent with the ${\pi }_1(1600)$ candidate. We also find a strangeness $\pm 1$ $J^P=1^{-}$ state with a mass close to 2 GeV.

We discuss heavy quarkonium production through parton fragmentation, including a review of arguments for the factorization of high-$p_T$ particles into fragmentation functions for hadronic initial states. We investigate the further factorization of fragmentation functions in the nonrelativistic QCD (NRQCD) formalism, and argue that this requires a modification of NRQCD octet production matrix elements to include non-Abelian phases, which makes them gauge invariant. We describe the calculation of uncanceled infrared divergences in fragmentation functions that must be factorized at next-to-next-to-leading order, and verify that they are absorbed into the new, gauge-invariant matrix elements.

A comprehensive parametrization of the color-singlet heavy quark free energy above $T_c$ is given, using the lattice data in quenched ($N_f=0$) and unquenched ($N_f=2$ and $N_f=3$) QCD. The corresponding (temperature dependent) potentials thus obtained are then inserted into the Schrödinger equation for charmonium and bottomonium in the deconfined phase of QCD. The solution of the equation provides an estimate of the melting temperature and of the radii for the different $c\overline{c}$ and $b\overline{b}$ bound states.

We study the thermodynamics of QCD in the limit of large flavor number ($N_f$) and test the proposal to resum the physics of hard thermal loops (HTL) through a nonperturbative expression for the entropy obtained from a $\Phi$-derivable two-loop approximation. The fermionic contribution to the entropy involves a full next-to-leading order evaluation of the asymptotic thermal quark mass, which is nonlocal, and for which only a weighted average value was known previously. For a natural choice of renormalization scale we find remarkably good agreement of the next-to-leading order HTL results for the fermion self-energy and in turn for the entropy with the respective exact large-$N_f$ results, even at very large coupling.

We present a new class of asymptotically flat charge static solutions in third order Lovelock gravity. These solutions present black hole solutions with two inner and outer event horizons, extreme black holes, or naked singularities provided the parameters of the solutions are chosen suitable. We find that the uncharged asymptotically flat solutions can present black holes with two inner and outer horizons. This kind of solution does not exist in Einstein or Gauss-Bonnet gravity, and it is a special effect in third order Lovelock gravity. We compute temperature, entropy, charge, electric potential, and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We also perform a stability analysis by computing the determinant of the Hessian matrix of the mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that there exists only an intermediate stable phase.

A first order symmetric hyperbolic tetrad formulation of the Einstein equations developed by Estabrook and Wahlquist and put into a form suitable for numerical relativity by Buchman and Bardeen (the WEBB formulation) is adapted to explicit spherical symmetry and tested for accuracy and stability in the evolution of spherically symmetric black holes (the Schwarzschild geometry). The lapse and shift, which specify the evolution of the coordinates relative to the tetrad congruence, are reset at frequent time intervals to keep the constant-time hypersurfaces nearly orthogonal to the tetrad congruence and the spatial coordinate satisfying a kind of minimal rate of strain condition. By arranging through initial conditions that the constant-time hypersurfaces are asymptotically hyperbolic, we simplify the boundary value problem and improve stability of the evolution. Results are obtained for both tetrad gauges (“Nester” and “Lorentz”) of the WEBB formalism using finite difference numerical methods. We are able to obtain stable unconstrained evolution with the Nester gauge for certain initial conditions, but not with the Lorentz gauge.

We determine the general conditions for the existence of Gödel, Einstein static, and de Sitter universes in gravity theories derived from a Lagrangian that is an arbitrary function of the scalar curvature and Ricci and Riemann curvature invariants. Explicit expressions for the solutions are found in terms of the parameters defining the Lagrangian. We also determine the conditions on the Lagrangian of the theory under which time-travel is allowed in the Gödel universes.

A long-lived very light pseudoscalar boson would favor lepton flavor violating transitions of charged leptons. Its implications on the $l_i\to l_j\gamma \gamma$ and $l_i\to l_j{e}^{+}{e}^{-}$ transitions are investigated. Assuming that $2m_e<m_{\varphi }<m_{\mu }$, it is found that the inequality $B(l_i\to l_j\gamma \gamma )<B(l_i\to l_j{e}^{+}{e}^{-})$ holds. The experimental constraints on the decays $l_i\to l_j\gamma$, $l_i\to l_j{l}_k{l}_k$, and $l_i\to l_j\gamma \gamma$ are used to bound the $\varphi l_i{l}_j$ couplings.

Resonant productions of the first generation scalar and vector diquarks at high energy hadron-hadron ($pp$), lepton-hadron ($ep$) and lepton-lepton ($e^{+}{e}^{-}$) colliders are investigated. Taking into account the hadronic component of the photon, diquarks can be produced resonantly in the lepton-hadron and lepton-lepton collisions. Production rates, decay widths and signatures of diquarks are discussed using the general, $\mathrm{SU}(3{)}_C\times \mathrm{SU}(2{)}_W\times \mathrm{U}(1{)}_Y$ invariant, effective Lagrangian. The corresponding dijet backgrounds are examined in the interested invariant mass regions. The attainable mass limits and couplings are obtained for the diquarks that can be produced in hadron collisions and in resolved photon processes. It is shown that hadron collider with center-of-mass energy $\sqrt{s}=14\mathrm{TeV}$ will be able to discover scalar and vector diquarks with masses up to $m_{DQ}=9\mathrm{TeV}$ for quark-diquark-quark coupling ${\alpha }_{DQ}=0.1$. Relatively, lighter diquarks can be probed at $ep$ and $e^{+}{e}^{-}$ collisions in more clear environment.

We obtain tree-level unitarity constraints for the most general Two-Higgs-Doublet Model (2HDM) with explicit $CP$-violation. We briefly discuss correspondence between possible violation of tree-level unitarity limitation and physical content of the theory.