The anti–de Sitter space/conformal field theory (AdS/CFT) correspondence may offer new and useful insights into the nonperturbative regime of strongly coupled gauge theories such as quantum chromodynamics (QCD). Recently, a modified soft-wall AdS/QCD model incorporated independent sources for explicit and spontaneous chiral symmetry breaking and linear confinement. This model contains a modified dilaton and higher-order interaction terms in the Lagrangian. Within this model we explore the radial pseudoscalar mass spectrum using two different representations of the pion field. We find the mass eigenvalues associated with each representation show the equivalence between the two, and we find good agreement with the pion masses. The Gell-Mann–Oakes–Renner (GOR) relation is naturally obtained.

We analyze the distribution of the chromoelectric field generated by a static quark-antiquark pair in the SU(3) vacuum and revisit previous results for SU(2). We find that the transverse profile of the flux tube resembles the dual version of the Abrikosov vortex field distribution. We give an estimate of the London penetration length of the chromoelectric field in the confined vacuum. We also speculate on the value of the ratio between the penetration lengths for SU(2) and SU(3) gauge theories.

We calculate the electromagnetic, axial, and pseudoscalar form factors of the nucleon to $\Delta (1232)$ transition using two dynamical light degenerate quarks and a dynamical strange quark simulated with the domain wall fermion action. Results are obtained at lattice spacings $a=0.114\mathrm{fm}$ and $a=0.084\mathrm{fm}$, with corresponding pion masses of 330 MeV and 297 MeV, respectively. High statistics measurements are achieved by utilizing the coherent sink technique. The dominant electromagnetic dipole form factor, the axial form factors and the pseudoscalar coupling are extracted to a good accuracy. This allows the investigation of the nondiagonal Goldberger-Treiman relation. Particular emphasis is given on the extraction of the subdominant electromagnetic quadrupole form factors and their ratio to the dominant dipole form factor, $R_{\mathrm{EM}}$ and $R_{\mathrm{SM}}$, measured in experiment.

A measurement of the atmospheric muon neutrino energy spectrum from 100 GeV to 400 TeV was performed using a data sample of about 18 000 up-going atmospheric muon neutrino events in IceCube. Boosted decision trees were used for event selection to reject misreconstructed atmospheric muons and obtain a sample of up-going muon neutrino events. Background contamination in the final event sample is less than 1%. This is the first measurement of atmospheric neutrinos up to 400 TeV, and is fundamental to understanding the impact of this neutrino background on astrophysical neutrino observations with IceCube. The measured spectrum is consistent with predictions for the atmospheric ${\nu }_{\mu }+{\overline{\nu }}_{\mu }$ flux.

We investigate finite-size effects on the phase structure of chiral and difermion condensates at finite temperature and density in the framework of the two-dimensional large-$N$ Nambu-Jona-Lasinio model. We take into account size-dependent effects by making use of zeta-function and compactification methods. The thermodynamic potential and the gap equations for the chiral and difermion condensed phases are then derived in the mean-field approximation. Size-dependent critical lines separating the different phases are obtained considering antiperiodic boundary conditions for the spatial coordinate.

We measure the recoil velocity as a function of spin for equal-mass, highly spinning black-hole binaries, with spins in the orbital plane, equal in magnitude, and opposite in direction. We confirm that the leading-order effect is linear in the spin and the cosine of angle between the spin direction and the infall direction at the merger. We find higher-order corrections that are proportional to the odd powers in both the spin and cosine of this angle. Taking these corrections into account, we predict that the maximum recoil will be $3680\pm 130\mathrm{km}{\mathrm{s}}^{-1}$.

We derive a general formula for the center-of-mass (CM) energy for the near-horizon collision of two particles of the same rest mass on the equatorial plane around a Kerr black hole. We then apply this formula to a particle which plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. It is found that the maximum value of the CM energy $E_{\mathrm{cm}}$ is given by $E_{\mathrm{cm}}/(2m_0)\simeq 1.40/\sqrt[4]{1-a_{*}^2}$ for a nearly maximally rotating black hole, where $m_0$ is the rest mass of each particle and $a_{*}$ is the nondimensional Kerr parameter. This coincides with the known upper bound for a particle which begins at rest at infinity within a factor of 2. Moreover, we also consider the collision of a particle orbiting the ISCO with another particle on the ISCO and find that the maximum CM energy is then given by $E_{\mathrm{cm}}/(2m_0)\simeq 1.77/\sqrt[6]{1-a_{*}^2}$. In view of the astrophysical significance of the ISCO, this result implies that particles can collide around a rotating black hole with an arbitrarily high CM energy without any artificial fine-tuning in an astrophysical context if we can take the maximal limit of the black hole spin or $a_{*}\to 1$. On the other hand, even if we take Thorne’s bound on the spin parameter into account, highly or moderately relativistic collisions are expected to occur quite naturally, for $E_{\mathrm{cm}}/(2m_0)$ takes 6.95 (maximum) and 3.86 (generic) near the horizon and 4.11 (maximum) and 2.43 (generic) on the ISCO for $a_{*}=0.998$. This implies that high-velocity collisions of compact objects are naturally expected around a rapidly rotating supermassive black hole. Implications to accretion flows onto a rapidly rotating black hole are also discussed.

We propose a cosmological model in the framework of the Poincaré gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in both curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar $R$ and the curvature pseudoscalar $X$ linearly and quadratically (including an $RX$ term) and (ii) pieces quadratic in the torsion vector $\mathcal{V}$ and the torsion axial vector $\mathcal{A}$ (including a $\mathcal{V}\mathcal{A}$ term). We show generally that in quadratic PG models we have nearly the same number of parity conserving terms (“world”) and of parity violating terms (“shadow world”). This offers new perspectives in cosmology for the coupling of gravity to matter and antimatter. Our specific model generalizes the fairly realistic “torsion cosmologies” of Shie-Nester-Yo (2008) and Chen et al. (2009). With a Friedman type ansatz for an orthonormal coframe and a Lorentz connection, we derive the two field equations of PG in an explicit form and discuss their general structure in detail. In particular, the second field equation can be reduced to first order ordinary differential equations for the curvature pieces $R(t)$ and $X(t)$. Including these along with certain relations obtained from the first field equation and curvature definitions, we present a first order system of equations suitable for numerical evaluation. This is deferred to the second, numerical part of this paper.

In the recent paper by Mielczarek et al. (Ref. [8]), an idea of the method which can be used to put some constraint for the reheating phase was proposed. Another method of constraining the reheating temperature has been recently studied by Martin and Ringeval (Ref. [17]). Both methods are based on observations of the cosmic microwave background (CMB) radiation. In this paper, we develop the idea introduced in this first article to put constraint on the reheating after the slow-roll inflation. We restrict our considerations to the case of a massive inflaton field. The method can be, however, easily extended to the different inflationary scenarios. As a main result, we derive an expression on the reheating temperature $T_{\mathrm{RH}}$. Surprisingly, the obtained equation is independent on the unknown number of relativistic degrees of freedom $g_{*}$ produced during the reheating. Based on this equation and the WMAP 7 observations, we find $T_{\mathrm{RH}}=3.5\times {10}^6\mathrm{GeV}$, which is consistent with the current constraints. The relative uncertainty of the result is, however, very high and equal to $\sigma (T_{\mathrm{RH}})/T_{\mathrm{RH}}\approx 53$. As we show, this uncertainty will be significantly reduced with future CMB experiments.

We study the potential energy between static charges in $G_2$ gluodynamics in three and four dimensions. Our work is based on an efficient local hybrid Monte Carlo algorithm and a multilevel Lüscher-Weisz algorithm with exponential error reduction to accurately measure expectation values of Wilson and Polyakov loops. Both in three and four dimensions we show that at intermediate scales the string tensions for charges in various $G_2$ representations scale with the second order Casimir. In three dimensions Casimir scaling is confirmed within 4% for charges in representations of dimensions 7, 14, 27, 64, 77, ${77}^{\prime }$, 182, and 189 and in four dimensions within 5% for charges in representations of dimensions 7, 14, 27, and 64. In three dimensions we detect string breaking for charges in the two fundamental representations. The scale for string breaking agrees very well with the mass of the created pair of glue lumps. Close to the string breaking distance Casimir scaling between adjoint and defining representation is violated by 2.5%. The analytical prediction for the continuum string tension is confirmed for the defining representation in three dimensions.

To estimate cosmological parameters from a given data set, we need to construct a likelihood function, which sometimes has a complicated functional form. We introduce the copula, a mathematical tool to construct an arbitrary multivariate distribution function from one-dimensional marginal distribution functions with any given dependence structure. It is shown that a likelihood function constructed by the so-called Gaussian copula can reproduce very well the $n$-dimensional probability distribution of the cosmic shear power spectrum obtained from a large number of ray-tracing simulations. This suggests that the Copula likelihood will be a powerful tool for future weak lensing analyses, instead of the conventional multivariate Gaussian likelihood.

We compute a variety of two and three-point real-time correlation functions for a strongly-coupled nonrelativistic field theory. We focus on the theory conjectured to be dual to the Schrödinger-invariant gravitational spacetime introduced by Balasubramanian, McGreevy, and Son, but our methods apply to a large class of nonrelativistic theories. At zero temperature, we obtain time-ordered, retarded, and Wightman nonrelativistic correlators for scalar operators of arbitrary conformal dimension directly in field theory by applying a certain lightlike Fourier-transform to relativistic conformal correlators, and we verify that nonrelativistic AdS/CFT reproduces the results. We compute thermal two and three-point real-time correlators for scalar operators dual to scalar fields in the black hole background which is the finite-temperature generalization of the Schrödinger spacetime. This is done by first identifying thermal real-time bulk-to-boundary propagators which, when combined with Veltman’s circling rules, yield two and three-point correlators. The two-point correlators we obtain satisfy the Kallen-Lehmann relations. We also give retarded and time-ordered three-point correlators.

One can define generalized models of gaugino condensation as theories that dynamically break a discrete $R$ symmetry but do not break supersymmetry. We consider general examples consisting of gauge and matter fields and the minimal number of gauge-singlet fields to avoid flat directions in the potential. We explore which $R$ symmetries can arise and their spontaneous breaking. In general, we find that the discrete symmetry is ${\mathbb{Z}}_{2b_{0}R}$, and the number of supersymmetric vacua is $b_0$, where $b_0$ is the coefficient of the one-loop beta function. Results are presented for various groups, including $SU(N_c)$, $SO(N_c)$, $Sp(2N_c)$, and $G_2$, for various numbers of flavors, $N_f$, by several methods. This analysis can also apply to the other exceptional groups and, thus, all simple Lie groups. We also comment on model-building applications where a discrete $R$ symmetry, broken by the singlet vacuum expectation values, can account for $\mu$-type terms and allow a realistic Higgs spectrum naturally.

Semiclassical gravity is investigated in a large class of asymptotically flat, static, spherically symmetric spacetimes including those containing static stars, black holes, and wormholes. Specifically the stress-energy tensors of massless free spin 0 and spin $1/2$ fields are computed to leading order in the asymptotic regions of these spacetimes. This is done for spin 0 fields in Schwarzschild spacetime using a WKB approximation. It is done numerically for the spin $1/2$ field in Schwarzschild, extreme Reissner-Nordström, and various wormhole spacetimes. And it is done by finding analytic solutions to the leading order mode equations in a large class of asymptotically flat static spherically symmetric spacetimes. Agreement is shown between these various computational methods. It is found that, for all of the spacetimes considered, the energy density and pressure in the asymptotic region are proportional to $r^{-5}$ to leading order. Furthermore, for the spin $1/2$ field and the conformally coupled scalar field, the stress-energy tensor depends only on the leading order geometry in the far field limit. This is also true for the minimally coupled scalar field for spacetimes containing either a static star or a black hole, but not for spacetimes containing a wormhole.

We investigate the group field theory formulation of the Engle-Pereira-Rovelli-Livine/Freidel-Krasnov (EPRL/FK spin-foam models. These models aim at a dynamical, i.e., nontopological formulation of 4D quantum gravity. We introduce a saddle point method for general group field theory amplitudes and compare it with existing results, in particular, for a second order correction to the EPRL/FK propagator.

The imminent detection of gravitational waves will trigger precision tests of gravity through observations of quasinormal ringing of black holes. While general relativity predicts just two polarizations of gravitational waves, the so-called plus and cross polarizations, numerous alternative theories of gravity predict up to six different polarizations which will potentially be observed in current and future generations of gravitational wave detectors. Bekenstein’s Tensor-Vector-Scalar (TeVeS) theory and its generalization fall into one such class of theory that predict the full gamut of six polarizations of gravitational waves. In this paper we begin the study of quasinormal modes (QNMs) in TeVeS by studying perturbations of the scalar field in a spherically symmetric background. We show that, at least in the case where superluminal propagation of perturbations is not present, black holes are generically stable to this kind of perturbation. We also make a unique prediction that, as the limit of the various coupling parameters of the theory tend to zero, the QNM spectrum tends to $1/\sqrt{2}$ times the QNM spectrum induced by scalar perturbations of a Schwarzschild black hole in general relativity due to the intrinsic presence of the background vector field. We further show that the QNM spectrum does not vary significantly from this value for small values of the theory’s coupling parameters, however can vary by as much as a few percent for larger, but still physically relevant parameters.

We study the Lamb shift of both freely falling and static two-level atoms in interaction with quantized conformally coupled massless scalar fields in the de Sitter-invariant vacuum. We find that the Lamb shifts of both freely falling and static atoms are in structural similarity to that of an inertial atom immersed in a thermal bath in a Minkowski spacetime. For the freely falling atom, the Lamb shift gets a correction as if it was immersed in a thermal bath at the Gibbons-Hawking temperature, thus revealing clearly the intrinsic thermal nature of de Sitter spacetime. For the static atom, the Lamb shift is affected by a combination of the effect of the intrinsic thermal nature of de Sitter spacetime and the Unruh effect associated with the inherent acceleration of the atom.

For the five-dimensional spacetimes whose four-dimensional sections are static, spherically symmetric ($SO(3)$), and flat asymptotically, we study the behavior of Arnowitt-Deser-Misner mass, tension, and momentum densities characterizing such asymptotically hypercylindrical metrics under boosts along the cylindrical axis. For such stringlike metrics two boost-invariant quantities are found, which are a sort of “string rest mass squared” and the sum of mass and tension densities. Analogous to the case of a moving point particle, we show that the asymptotically hypercylindrical geometries can be classified into three types depending on the value of the string rest mass squared, namely, “ordinary string”, “null string” and “tachyonlike string” geometries. This asymptotic analysis shows that the extraordinary metrics reported recently by some of the authors belong to the tachyonlike string. Consequently, it is likely that such extraordinary solutions are the final states of tachyonic matter collapse. We also report two new vacuum solutions which belong to the null string and the tachyonlike string, respectively.

We study in detail the properties of gravitationally bounded multistate configurations, made of spin-zero bosons, in the Newtonian regime. We show that the properties of such configurations, in particular, their stability, depend upon how the particles are distributed in the different states they are composed of. Numerical techniques are used to distinguish between stable and unstable solutions, and to determine the final configurations they evolve towards. Multistate equilibrium configurations could be used as models of galactic halos made of scalar field dark matter, whose rotation curves appear more realistic than in the case of single-state configurations.

We investigate a Friedmann universe filled with a tachyon scalar field, which behaved as dustlike matter in the past, while it is able to accelerate the expansion rate of the Universe at late times. The comparison with type Ia supernovae (SNIa) data allows for evolutions driving the Universe into a Big Brake. Some of the evolutions leading to a Big Brake exhibit a large variation of the equation of state parameter at low redshifts, which is potentially observable with future data, though hardly detectable with present SNIa data. The soft Big Brake singularity occurs at finite values of the scale factor, vanishing energy density and Hubble parameter, but diverging deceleration and infinite pressure. We show that the geodesics can be continued through the Big Brake and that our model universe will recollapse eventually in a Big Crunch. Although the time to the Big Brake strongly depends on the present values of the tachyonic field and of its time derivative, the time from the Big Brake to the Big Crunch represents a kind of invariant time scale for all field parameters allowed by SNIa.