We discuss in the planar approximation the effect of double-trace deformations on conformal field theories. We show that this large class of models posses a conformal window describing a nontrivial flow between two fixed points of the renormalization group and reveal the presence of a resonance which we associate to the remnant of a dilaton pole. As the conformal window shrinks to zero measure, the theory undergoes a conformal phase transition separating a symmetric from a nonsymmetric phase. The recently conjectured strongly coupled branch of nonsupersymmetric, non-Abelian gauge theories with a large number of flavors is analyzed in light of these results, and a model for the strong branch is proposed. Some phenomenological implications in the context of unparticle physics are also emphasized.

We study the geodesic equation in the space-time of a Kerr black hole pierced by an infinitely thin cosmic string and give the complete set of analytical solutions of this equation for massive and massless particles in terms of Mino time that allows one to decouple the $r$ and $\theta$ components of the geodesic equation. The solutions of the geodesic equation can be classified according to the particle’s energy and angular momentum, the mass and angular momentum per mass of the black hole. We give examples of orbits showing the influence of the cosmic string. We also discuss the perihelion shift and the Lense-Thirring effect for bound orbits and show that the presence of a cosmic string enhances both effects. Comparing our results with experimental data from the LAGEOS satellites we find an upper bound on the energy per unit length of a string piercing the earth which is approximately ${10}^{16}\mathrm{kg}/\mathrm{m}$. Our work has also applications to the recently suggested explanation of the alignment of the polarization vector of quasars using remnants of cosmic string decay in the form of primordial magnetic field loops.

The inspiral of a stellar compact object into a massive black hole, an extreme-mass-ratio inspiral, is one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna. We expect to be able to detect and analyze many cycles of these slowly inspiraling systems, which makes them truly high-precision tools for gravitational-wave astronomy. To that end, the use of very precise theoretical waveform templates in the data analysis is required. To build them, we need to have a deep understanding of the gravitational backreaction mechanism responsible for the inspiral. The self-force approach describes the inspiral as the action of a local force that can be obtained from the regularization of the perturbations created by the stellar compact object on the massive black hole geometry. In this paper we extend a new time-domain technique for the computation of the self-force from the circular case to the case of eccentric orbits around a nonrotating black hole. The main idea behind our scheme is to use a multidomain framework in which the small compact object, described as a particle, is located at the interface between two subdomains. Then, the equations at each subdomain are homogeneous wave-type equations, without distributional sources. In this particle-without-particle formulation, the solution of the equations is smooth enough to provide good convergence properties for the numerical computations. This formulation is implemented by using a pseudospectral collocation method for the spatial discretization, combined with a Runge-Kutta algorithm for the time evolution. We present results from several simulations of eccentric orbits in the case of a scalar charged particle around a Schwarzschild black hole, an excellent test bed model for testing the techniques for self-force computations. In particular, we show the convergence of the method and its ability to resolve the field and its derivatives across the particle location. Finally, we provide numerical values of the self-force for different orbital parameters.

Nonsingular cosmologies are investigated in the framework of $f(R)$ gravity within the first order formalism. General conditions for bounces in isotropic and homogeneous cosmology are presented. It is shown that only a quadratic curvature correction is needed to predict a bounce in a flat or to describe cyclic evolution in a curved dust-filled universe. Formalism for perturbations in these models is set up. In the simplest cases, the perturbations diverge at the turnover. Conditions to obtain smooth evolution are derived.

We build five-dimensional spherically symmetric wormholes within the DGP theory. We calculate the energy localized on the shell, and we find that the wormholes could be supported by matter not violating the energy conditions. We also show that solitonic shells characterized by zero pressure and zero energy can exist; thereafter we make some observations regarding their dynamic on the phase plane. In addition, we concentrate on the mechanical stability of wormholes under radial perturbation preserving the original spherical symmetry. In order to do that, we consider linearized perturbations around static solutions. We obtain that for certain values of the mass parameter $\mu$ and the crossover scale $r_c$ stable wormholes exist with very small values of squared speed sound. Unlike the case of Einstein’s gravity, this type of wormholes fulfills the energy conditions. Finally, we show that the gravitational field associated with these wormhole configurations is attractive for $\mu >0$.

The components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a perfect fluid with equation of state $p=\frac{1}{3}\rho$ in the flat Friedmann-Robertson-Walker quantum cosmological model. The quantum behavior of the equation of state and energy conditions are then studied, and it is shown that the energy conditions are violated since the singularity is removed with the introduction of quantum cosmology, but in the classical limit both the equation of state and the energy conditions behave as in the classical model. We also calculate the expectation value of the scale factor for several wave packets in the many-worlds interpretation in order to show the independence of the nonsingular character of the quantum cosmological model with respect to the wave packet representing the wave function of the Universe. It is also shown that, with the introduction of nonnormalizable wave packets, solutions of the Wheeler-DeWitt equation, the singular character of the scale factor, can be recovered in the ontological interpretation.

We place functional constraints on the shape of the inflaton potential from the cosmic microwave background through a variant of the generalized slow-roll approximation that allows large amplitude, rapidly changing deviations from scale-free conditions. Employing a principal component decomposition of the source function $G^{\prime }\approx 3(V^{\prime }/V{)}^2-2V^{\prime \prime }/V$ and keeping only those measured to better than 10% results in 5 nearly independent Gaussian constraints that may be used to test any single-field inflationary model where such deviations are expected. The first component implies $<3\%$ variations at the 100 Mpc scale. One component shows a 95% CL preference for deviations around the 300 Mpc scale at the $\sim 10\%$ level but the global significance is reduced considering the 5 components examined. This deviation also requires a change in the cold dark matter density which in a flat $\Lambda \mathrm{CDM}$ model is disfavored by current supernova and Hubble constant data and can be tested with future polarization or high multipole temperature data. Its impact resembles a local running of the tilt from multipoles 30–800 but is only marginally consistent with a constant running beyond this range. For this analysis, we have implemented a $\sim 40\times$ faster WMAP7 likelihood method which we have made publicly available.

Subject to some relatively mild assumptions, we derive the complete form of all timelike half-supersymmetric solutions to $\mathcal{N}=2$, $D=4$ gauged supergravity coupled to an arbitrary number of Abelian vector multiplets. This is done using spinorial geometry techniques. Explicit examples are given for a simple prepotential. Among the solutions, there are near-horizon geometries of extremal rotating supersymmetric black holes still to be discovered, with a nontrivial dependence of the scalar fields on one of the horizon coordinates.

We consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients and reinvestigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities. We calculate explicitly the self-interactions of the helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2 modes. We show that ghostlike pathologies in these interactions disappear for special choices of the polynomial interactions and argue that this result remains true to all orders in the decoupling limit. Moreover, we show that the linear and some of the nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, which then naturally generates the cubic, quartic, and quintic Galileon interactions, introduced in a different context. We also point out that the mixing between the helicity-0 and -2 modes can be at most quartic in the decoupling limit. Finally, we discuss the implications of our findings for the consistency of the effective field theory away from the decoupling limit, and for the Boulware-Deser problem.

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti–de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler space at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.

We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the “twisted geometries” and derive a simple relation between these and Regge geometries.

We prove the uniqueness theorem for the stationary axisymmetric black hole solution in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory. We consider both the nonextremal and extremal Kerr-Sen black hole solutions.

There have been the approximate analytic solution [V. Silveira and I. Waga, Phys. Rev. D 50, 4890 (1994).] and several approximate analytic forms [W. J. Percival, Astron. Astrophys. 443, 819 (2005).][S. M. Carroll, W. H. Press, and E. L. Turner, Annu. Rev. Astron. Astrophys. 30, 499 (1992).][S. Basilakos, Astrophys. J. 590, 636 (2003).] of the growth factor $D_g$ for the general dark energy models with the constant values of its equation of state ${\omega }_{\mathrm{de}}$ after Heath found the exact integral form of the solution of $D_g$ for the Universe including the cosmological constant or the curvature term. Recently, we obtained the exact analytic solutions of the growth factor for both ${\omega }_{\mathrm{de}}=-1$ or $-\frac{1}{3}$ [S. Lee and K.-W. Ng, arXiv:0905.1522.] and the general dark energy models with the constant equation of state ${\omega }_{\mathrm{de}}$ [S. Lee and K.-W. Ng, Phys. Lett. B 688, 1 (2010).] independently. We compare the exact analytic solution of $D_g$ with the other well known approximate solutions. We also prove that the analytic solutions for ${\omega }_{\mathrm{de}}=-1$ or $-\frac{1}{3}$ in [S. Lee and K.-W. Ng, arXiv:0905.1522.] are the specific solutions of the exact solutions of the growth factor for general ${\omega }_{\mathrm{de}}$ models in [S. Lee and K.-W. Ng, Phys. Lett. B 688, 1 (2010).] even though they look quite different. Comparison with the numerical solution obtained from the public code is done. We also investigate the possible extensions of the exact solution of $D_g$ to the time-varying ${\omega }_{\mathrm{de}}$ for the comparison with observations.

About 90% of $B_s{\overline{B}}_s$ pairs produced at the ${\rm Y}(5s)$ resonance are initially $B_s^{*}{\overline{B}}_s^{*}$ pairs which decay radiatively to $B_s{\overline{B}}_s$. This implies that the $B_s{\overline{B}}_s$ pair will then be in an eigenstate of charge conjugation (i.e. $C=-1$) and therefore in an entangled state. This allows for a determination of $\Delta {\Gamma }_s/{\Gamma }_s$ and the $CP$ phase using a number of possible correlations between the decays of the two $B_s$ mesons. In particular, we consider the time integrated correlation, the time ordering asymmetry, and the time ordering-charge asymmetry, which in addition to time ordering distinguishes $B_s$ from ${\overline{B}}_s$, for various combinations of final states. With the statistics of about $O({10}^7–{10}^8)$ ${\rm Y}(5s)$ events available at $B$ factories, we find that the time ordering asymmetry between suitably defined hadronic and flavor specific (tagging) decays offers a promising method for determining the width difference. The corresponding time ordering-charge asymmetry can also bound the mixing phase. Similar observables involving exclusive decays are also considered. At the super $B$ factories with $O(50)$ times greater luminosity time ordering and time ordering-charge asymmetries between inclusive and exclusive modes may also provide additional bounds on the phases in those decays.

The standard model predicts a very small $CP$ violation phase $\sin 2{\Phi }_{B_s}^{\mathrm{SM}}\simeq -0.04$ in $B_s-{\overline{B}}_s$ mixing. Any finite value of ${\Phi }_{B_s}$ measured at the Tevatron would imply new physics. With recent hints for finite $\sin 2{\Phi }_{B_s}$, we reconsider the possibility of a fourth generation. As recent direct search bounds have become considerably heavier than 300 GeV, we take the $t^{\prime }$ mass to be near the unitarity bound of 500 GeV. Combining the measured values of $\Delta m_{B_s}$ with $\mathcal{B}(B\to X_s{\ell }^{+}{\ell }^{-})$, together with typical $f_{B_s}$ values, we find a sizable $\sin 2{\Phi }_{B_s}^{\mathrm{SM}4}\sim -0.33$. Using $m_{b^{\prime }}=480\mathrm{GeV}$, we extract the range $0.06<|V_{t^{\prime }b}|<0.13$ from the constraints of $\Gamma (Z\to b\overline{b})$, $\Delta m_D$, and $\mathcal{B}(K^{+}\to {\pi }^{+}\nu \overline{\nu })$. This illustrates how the $4\times 4$ mixing matrix can be determined in the future, once $m_{t^{\prime }}$ and $m_{b^{\prime }}$ are known. A crucial future measurement would be $\mathcal{B}(K_L\to {\pi }^0\nu \overline{\nu })$, which would determine $V_{t^{\prime }d}$.

We study the string tension as a function of temperature, fitting the SU(3) lattice QCD finite temperature free energy potentials computed by the Bielefeld group. We compare the string tension points with order parameter curves of ferromagnets, superconductors, or string models, all related to confinement. We also compare the SU(3) string tension with the one of SU(2) lattice QCD. With the curve providing the best fit to the finite temperature string tensions, the spontaneous magnetization curve, we then show how to include finite temperature, in the state of the art confining and chiral invariant quark models.

Chiral effective field theory ($\chi \mathrm{EFT}$) complements numerical simulations of quantum chromodynamics (QCD) on a space-time lattice. It provides a model-independent formalism for connecting lattice simulation results at finite volume and a variety of quark masses to the physical world. The asymptotic nature of the chiral expansion places the focus on the first few terms of the expansion. Thus, knowledge of the power-counting regime (PCR) of $\chi \mathrm{EFT}$, where higher-order terms of the expansion may be regarded as negligible, is as important as knowledge of the expansion itself. Through the consideration of a variety of renormalization schemes and associated parameters, techniques to identify the PCR where results are independent of the renormalization scheme are established. The nucleon mass is considered as a benchmark for illustrating this general approach. Because the PCR is small, the numerical simulation results are also examined to search for the possible presence of an intrinsic scale which may be used in a nonperturbative manner to describe lattice simulation results outside of the PCR. Positive results that improve on the current optimistic application of chiral perturbation theory ($\chi \mathrm{PT}$) beyond the PCR are reported.

We analyze the single transverse-spin asymmetry (SSAs) for inclusive hadron production in the $pp$ collision at RHIC based on the twist-3 mechanism in QCD. As an origin of SSAs, we take into account of all kinds of pole contributions associated with the twist-3 quark-gluon correlation functions in the polarized proton. By the inclusion of the soft-fermion-pole contribution in addition to the soft-gluon-pole contribution, we find SSAs observed at RHIC are better described for all kinds of mesons. $P_T$ dependence of the asymmetry and the comparison with the FNAL data are also presented.

The degeneracy among parity pairs systematically observed in the $N$ and $\Delta$ spectra is interpreted to hint on a possible conformal symmetry realization in the light flavor baryon sector in line with ${\mathrm{AdS}}_5/{\mathrm{CFT}}_4$. The case is made by showing that all the observed $N$ and $\Delta$ resonances with masses below 2500 MeV distribute fairly well each over the first levels of a unitary representation of the conformal group, a representation that covers the spectrum of a quark-diquark system, placed directly on a conformally compactified Minkowski spacetime, ${\mathbf{R}}^1\otimes S^3$, as approached from the ${\mathrm{AdS}}_5$ cone. The free geodesic motion on the $S^3$ manifold is described by means of the scalar conformal equation there, which is of the Klein-Gordon–type. The equation is then gauged by the curved Coulomb potential that has the form of a cotangent function. Conformal symmetry is not exact, this because the gauge potential slightly modifies the conformal centrifugal barrier of the free geodesic motion. Thanks to this, the degeneracy between $P_{11}-S_{11}$ pairs from same level is relaxed, while the remaining states belonging to same level remain practically degenerate. The model describes the correct mass ordering in the $P_{11}-S_{11}$ pairs through the spectra as a combined effect of the above conformal symmetry breaking, on the one side, and a parity change of the diquark from a scalar at low masses, to a pseudoscalar at higher masses, on the other. The quality of the wave functions is illustrated by calculations of realistic mean square charge radii and electric charge form factors on the examples of the proton, and the protonic $P_{11}(1440)$, and $S_{11}(1535)$ resonances. The scheme also allows for a prediction of the dressing function of an effective instantaneous gluon propagator from the Fourier transform of the gauge potential. We find a dressing function that is finite in the infrared and tends to zero at infinity.

We analyze the leptonic sector in the left-right symmetric model dressed with a $(Z_2{)}^3$ discrete symmetry which realizes, after weak spontaneous breaking, a small broken $\mu \leftrightarrow \tau$ symmetry that is suggested to explain observable neutrino oscillation data. $\mu \leftrightarrow \tau$ symmetry is broken at tree level in the effective neutrino mass matrix due to the mass difference ${\tilde{m}}_{\tau }\ne {\tilde{m}}_{\mu }$ in the diagonal Dirac mass terms, whereas all lepton mixings arise from a Majorana mass matrix. In the limit of a small breaking we determined ${\theta }_{13}$, and the deviation from the maximal value of ${\theta }_{23}$, in terms of the light neutrino hierarchy scale, $m_3$, and a single free parameter $h_s$ of the model.