We give a general procedure to obtain non perturbative evolution operators in closed form for quantized linearly polarized two-Killing vector reductions of general relativity with a cosmological interpretation. We study the representation of these operators in Fock spaces and discuss in detail the conditions leading to unitary evolutions.

We consider the simplest scenario when black strings/cigars penetrate the cosmological brane. As a result, the brane has a Swiss-cheese structure, with Schwarzschild black holes immersed in a Friedmann-Lemaître-Robertson-Walker brane. There is no dark radiation in the model, the cosmological regions of the brane are characterized by a cosmological constant $\Lambda$ and flat spatial sections. Regardless of the value of $\Lambda$, these brane-world universes forever expand and forever decelerate. The totality of source terms in the modified Einstein equation sum up to a dust, establishing a formal equivalence with the general relativistic Einstein-Straus model. However in this brane-world scenario with black strings the evolution of the cosmological fluid strongly depends on $\Lambda$. For $\Lambda \le 0$ it has positive energy density $\rho$ and negative pressure $p$ and at late times it behaves as in the Einstein-Straus model. For (not too high) positive values of $\Lambda$ the cosmological evolution begins with positive $\rho$ and negative $p$, but this is followed by an epoch with both $\rho$ and $p$ positive. Eventually, $\rho$ becomes negative, while $p$ stays positive. A similar evolution is present for high positive values of $\Lambda$, however in this case the evolution ends in a pressure singularity, accompanied by a regular behavior of the cosmic acceleration. This is a novel type of singularity appearing in brane-worlds.

We investigate gravitational waves from a dust disk around a Schwarzschild black hole to focus on whether we can extract any of its physical properties from a direct detection of gravitational waves. We adopt a black hole perturbation approach in a time domain, which is a satisfactory approximation to illustrate a dust disk in a supermassive black hole. We find that we can determine the radius of the disk by using the power spectrum of gravitational waves and that our method to extract the radius works for a disk of arbitrary density distribution. Therefore we believe a possibility exists for determining the radius of the disk from a direct observation of gravitational waves detected by the Laser Interferometer Space Antenna.

The coincidence problem of late cosmic acceleration is a serious riddle in connection with our understanding of the evolution of the Universe. In this paper we show that an interaction between the dark energy component (either phantom or quintessence) and dark matter can alleviate it. In this scenario the baryon component is independently conserved. This generalizes a previous study [S. del Campo, R. Herrera, and D. Pavón, Phys. Rev. D 71, 123529 (2005).] in which neither baryons nor phantom energy were considered.

Supersymmetry (SUSY) broken by anomaly mediation suffers from tachyonic slepton masses. A possible solution to this problem results in “decoupling,” i.e., the first two generations of sfermions are much heavier than the third one. We note that in this scenario a sizable loop-induced contribution to the neutrino mass matrix results. As an application of this scenario we take advantage of the fact that the decoupling evidently does not obey 2–3 generation exchange symmetry. In the neutrino sector, this 2–3 symmetry (or $\mu –\tau$ symmetry) is a useful Ansatz to generate zero ${\theta }_{13}$ and maximal ${\theta }_{23}$. The induced deviations from these values are given for some examples, including bimaximal and tribimaximal mixing. We are thereby able to link SUSY breaking to the small parameters (including possibly the solar mass splitting) of the neutrino sector.

We examine whether the fact that QCD is chirally invariant at short distances necessarily leads to the prediction that hadrons form approximate parity doublets, as has been recently put forward by Glozman and collaborators. We show that this is not the case, and we exhibit some of the pitfalls of trying to link the operator product expansion to the hadron spectrum. We illustrate our arguments within a model for scalar and pseudoscalar mesons used recently by Shifman to argue for parity doubling. We find that, whatever the experimental situation may be, there is no theoretical basis for parity doubling based on the use of the operator product expansion.

It is shown that fine-tuning of the Higgs parameters stronger than a few percent is required at best in the models with gauge mediated supersymmetry breaking. With the aim of solving this problem, we consider a new type of models in which the top Yukawa coupling is induced at TeV scale through mass mixing with unknown matter fields. Then it is found that the fine-tuning problem can be eliminated essentially. We discuss some phenomenological features of this model and also consider the extension to the next-to-minimal models.

We perform a first precision calculation of the transverse-momentum ($q_T$) distribution of slepton pair and slepton-sneutrino associated production at the CERN Large Hadron Collider. We implement soft-gluon resummation at the next-to-leading logarithmic level and consistently match the obtained result to the pure fixed-order perturbative result at leading order in the QCD coupling constant, i.e. $\mathcal{O}({\alpha }_s)$. We give numerical predictions for ${\tilde{\tau }}_1{\tilde{\tau }}_1^{*}$ and ${\tilde{\tau }}_1{\tilde{\nu }}_{\tau }^{*}+{\tilde{\tau }}_1^{*}{\tilde{\nu }}_{\tau }$ production, also implementing recent parametrizations of nonperturbative effects. The results show a relevant contribution of resummation both in the small and intermediate $q_T$-regions and little dependence on unphysical scales and nonperturbative contributions.

We further investigate center vortex percolation and Coulomb gauge remnant symmetry breaking in the SU(2) gauge-Higgs model. We show that string breaking is visible in Polyakov line correlators on the center-projected lattice, that our usual numerical tests successfully relate P-vortices to center vortices, and that vortex removal removes the linear potential, as in the pure-gauge theory. This data suggests that global center symmetry is not essential to the vortex confinement mechanism. But we also find that the line of vortex percolation-depercolation transitions, and the line of remnant symmetry-breaking transitions, do not coincide in the SU(2)-Higgs phase diagram. This nonuniqueness of transition lines associated with nonlocal order parameters favors a straightforward interpretation of the Fradkin-Shenker theorem, namely: there is no unambiguous distinction, in the SU(2) gauge-Higgs models, between a “confining” phase and a Higgs phase.

Motivated by questions about the QCD deconfining phase transition, we studied in two previous papers model A (Glauber) dynamics of 2D and 3D Potts models, focusing on structure factor evolution under heating (heating in the gauge theory notation, i.e., cooling of the spin systems). In the present paper we set for 3D Potts models (Ising and 3-state) the scale of the dynamical effects by comparing to equilibrium results at first and second order phase transition temperatures, obtained by reweighting from a multicanonical ensemble. Our finding is that the dynamics entirely overwhelms the critical and noncritical equilibrium effects. In the second half of the paper we extend our results by investigating the Glauber dynamics of pure SU(3) lattice gauge on $N_{\tau }{N}_{\sigma }^3$ lattices directly under heating quenches from the confined into the deconfined regime. The exponential growth factors of the initial response are calculated, which give Debye screening mass estimates. The quench leads to competing vacuum domains of distinct $Z_3$ triality, which delay equilibration of pure gauge theory forever, while their role in full QCD remains a subtle question. As in spin systems we find for pure SU(3) gauge theory a dynamical growth of structure factors, reaching maxima which scale approximately with the volume of the system, before settling down to equilibrium. Their influence on various observables is studied and different lattice sizes are simulated to illustrate an approach to a finite volume continuum limit. Strong correlations are found during the dynamical process, but not in the deconfined phase at equilibrium.

We improve, in the energy region between the $\overline{K}K$ threshold and $\sim 1.4\mathrm{GeV}$, the energy-dependent phase shift analysis of $\pi \pi$ scattering presented in a previous paper. For the S0 wave, we have included more data above the $\overline{K}K$ threshold and we have taken into account systematically the elasticity data on the reaction $\pi \pi \to \overline{K}K$. We here made a coupled channel fit. For the D0 wave, we have considered information on low energy parameters, and imposed a better fit to the $f_2$ resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for $s^{1/2}\ge 1.42\mathrm{GeV}$, which we also carry out. We show that this more realistic input produces $\pi \pi$ scattering amplitudes that satisfy better forward dispersion relations, particularly for ${\pi }^0{\pi }^0$ scattering.

We derive an inequality for the distribution of quarks with nonzero orbital angular momentum, and thus demonstrate, in a model-independent way, that a nonvanishing anomalous magnetic moment requires both a nonzero size of the target as well as the presence of wave function components with quark orbital angular momentum $L_z^q>0$.

Mixing of active neutrinos with sterile ones generate “induced” contributions to the mass matrix of active neutrinos $\sim m_S{sin}^2{\theta }_{aS}$, where $m_S$ is the Majorana mass of the sterile neutrino and ${\theta }_{aS}$ is the active-sterile mixing angle. We study possible effects of the induced matrix which can modify substantially the implications of neutrino oscillation results. We have identified the regions of $m_S$ and ${sin}^2{\theta }_{aS}$ where the induced matrix (i) provides the dominant structures, (ii) gives the subdominant effects, and (iii) where its effects can be neglected. The induced matrix can be responsible for peculiar properties of the lepton mixing and neutrino mass spectrum, in particular, it can generate the tribimaximal mixing. We update and discuss bounds on the induced masses from laboratory measurements, astrophysics, and cosmology. We find that substantial impact of the induced matrix is possible if $m_S\sim (0.1–0.3)\mathrm{eV}$ and ${sin}^2{\theta }_{aS}\sim {10}^{-3}–{10}^{-2}$ or $m_S\ge 300\mathrm{MeV}$ and ${sin}^2{\theta }_{aS}\le {10}^{-9}$. The bounds can be relaxed in cosmological scenarios with low reheating temperature, if sterile neutrinos decay sufficiently fast, or their masses change with time.

We report on a study of the decay ${\overline{B}}^0\to D^{*+}\omega {\pi }^{-}$ with the BABAR detector at the PEP-II $B$-factory at the Stanford Linear Accelerator Center. Based on a sample of $232\times {10}^6$ $B\overline{B}$ decays, we measure the branching fraction $\mathcal{B}({\overline{B}}^0\to D^{*+}\omega {\pi }^{-})=(2.88\pm 0.21(\mathrm{stat}.)\pm 0.31(\mathrm{syst}.))\times {10}^{-3}$. We study the invariant mass spectrum of the $\omega {\pi }^{-}$ system in this decay. This spectrum is in good agreement with expectations based on factorization and the measured spectrum in ${\tau }^{-}\to \omega {\pi }^{-}{\nu }_{\tau }$. We also measure the polarization of the $D^{*+}$ as a function of the $\omega {\pi }^{-}$ mass. In the mass region 1.1 to 1.9 GeV we measure the fraction of longitudinal polarization of the $D^{*+}$ to be ${\Gamma }_L/\Gamma =0.654\pm 0.042(\mathrm{stat}.)\pm 0.016(\mathrm{syst}.)$. This is in agreement with the expectations from heavy-quark effective theory and factorization assuming that the decay proceeds as ${\overline{B}}^0\to D^{*+}\rho (1450{)}^{-}$, $\rho (1450{)}^{-}\to \omega {\pi }^{-}$.

It is found the most general local form of the 11-dimensional supergravity backgrounds which, by reduction along one isometry, gives rise to IIA supergravity solutions with a RR field and a nontrivial dilaton, and for which the condition $F^{(1,1)}=0$ holds.This condition is stronger than the usual condition $F^{ab}{J}_{ab}=0$, required by supersymmetry. It is shown that these D6 wrapped backgrounds arise from the direct sum of the flat Minkowski metric with certain $G_2$ holonomy metrics admitting an $U(1)$ action, with a local form found by Apostolov and Salamon. Indeed, the strong supersymmetry condition is equivalent to the statement that there is a new isometry on the $G_2$ manifold, which commutes with the old one; therefore these metrics are inherently toric. An example that is asymptotically Calabi-Yau metric is presented. We find other $G_2$ metrics which give rise to half-flat $SU(3)$ structures. All these examples possess an $U(1)\times U(1)\times U(1)$ isometry subgroup. Supergravity solutions without fluxes corresponding to these $G_2$ metrics are constructed. The presence of a $T^3$ subgroup of isometries permits to apply the $\gamma$-deformation technique in order to generate new supergravity solutions with fluxes.

We apply the transformation of the mixing azimuthal and internal coordinate or the mixing time and internal coordinate to the 11D M theory with a stack of $\mathrm{M}2\mathrm{\text{−}}\mathrm{branes}\perp \mathrm{M}2\mathrm{\text{−}}\mathrm{branes}$, then through the mechanism of Kaluza-Klein reduction and a series of the T duality we obtain the corresponding background of a stack of $\mathrm{D}1\mathrm{\text{−}}\mathrm{branes}\perp \mathrm{D}5\mathrm{\text{−}}\mathrm{branes}$ which, in the near-horizon limit, becomes the magnetic or electric Melvin field deformed ${\mathrm{AdS}}_3\times S^3\times T^4$. We find the giant graviton solution in the deformed spacetime and see that the configuration whose angular momentum is within a finite region could have a fixed size and become more stable than the pointlike graviton, in contrast to the undeformed giant graviton which only exists when its angular momentum is a specific value and could have arbitrary size. We discuss in detail the properties of how the electric/magnetic Melvin field will affect the size of the giant gravitons. We also adopt an ansatz to find the classical string solutions which are rotating in the deformed $S^3$ with an angular momentum in the rotation plane. The spinning string and giant graviton solutions we obtained show that the external magnetic/electric flux will increase the solution energy. Therefore, from the anti-de Sitter (AdS)/conformal field theory (CFT) point of view, the corrections of the anomalous dimensions of operators in the dual field theory will be positive. Finally, we also see that the spinning string and giant graviton in the near-horizon spacetime of Melvin field deformed D5-branes background have similar properties to those in the deformed ${\mathrm{AdS}}_3\times S^3\times T^4$.

In this paper, we find quasinormal spectrum of the massive scalar field in the background of the Kerr black holes. We show that all found modes are damped under the quasinormal modes boundary conditions when $\mu M\lesssim 1$, thereby implying stability of the massive scalar field. This complements the region of stability determined by the Beyer inequality for large masses of the field. We show that, similar to the case of a nonrotating black hole, the massive term of the scalar field does not contribute in the regime of high damping. Therefore, the high damping asymptotic should be the same as for the massless scalar field.

First, we construct the Taub-NUT/bolt solutions of $(2k+2)$-dimensinal Einstein-Maxwell gravity, when all the factor spaces of $2k$-dimensional base space $\mathcal{B}$ have positive curvature. These solutions depend on two extra parameters, other than the mass and the NUT charge. These are electric charge $q$ and electric potential at infinity $V$. We investigate the existence of Taub-NUT solutions and find that in addition to the two conditions of uncharged NUT solutions, there exist two extra conditions. These two extra conditions come from the regularity of vector potential at $r=N$ and the fact that the horizon at $r=N$ should be the outer horizon of the NUT charged black hole. We find that the NUT solutions in $2k+2$ dimensions have no curvature singularity at $r=N$, when the $2k$-dimensional base space is chosen to be ${\mathbb{C}\mathbb{P}}^{2k}$. For bolt solutions, there exists an upper limit for the NUT parameter which decreases as the potential parameter increases. Second, we study the thermodynamics of these spacetimes. We compute temperature, entropy, charge, electric potential, action and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We perform a stability analysis by computing the heat capacity, and show that the NUT solutions are not thermally stable for even $k$’s, while there exists a stable phase for odd $k$’s, which becomes increasingly narrow with increasing dimensionality and wide with increasing $V$. We also study the phase behavior of the 4 and 6 dimensional bolt solutions in canonical ensemble and find that these solutions have a stable phase, which becomes smaller as $V$ increases.

Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors and significantly extend the known results on the resolution of the big bang singularity. Specifically, the following results are established for the homogeneous isotropic model with a massless scalar field: (i) the scalar field is shown to serve as an internal clock, thereby providing a detailed realization of the “emergent time” idea; (ii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously; (iii) the Hamiltonian constraint is solved numerically to show that the big bang is replaced by a big bounce. Thanks to the nonperturbative, background independent methods, unlike in other approaches the quantum evolution is deterministic across the deep Planck regime. Our constructions also provide a conceptual framework and technical tools which can be used in more general models. In this sense, they provide foundations for analyzing physical issues associated with the Planck regime of loop quantum cosmology as a whole.

Discontinuities in nonlinear field theories propagate through null geodesics in an effective metric that depends on its dynamics and on the background geometry. Once information of the geometry of the universe comes mostly from photons, one should carefully analyze the effects of possible nonlinearities on electrodynamics in the cosmic geometry. Such a phenomenon of induced metric is rather general and may occur for any nonlinear theory independently of its spin properties. We limit our analysis here to the simplest case of nonlinear scalar field. We show that a class of theories that have been analyzed in the literature, having regular configuration in the Minkowski space-time background, is such that the field propagates like free waves in an effective de Sitter geometry. The observation of these waves would lead us to infer, erroneously, that we live in a de Sitter universe.