Small oscillations of current-carrying string loops around stable equilibrium positions corresponding to minima of the effective potential in the equatorial plane of the Kerr black holes are studied using the perturbation method. In the lowest approximation, two uncoupled harmonic oscillators are obtained that govern the radial and vertical oscillations; the higher-order terms determine nonlinear phenomena and transition to chaotic motion through quasiperiodic stages of the oscillatory motion. The radial profiles of frequencies of the radial and vertical harmonic oscillations that are also relevant in the quasiperiodic stages of the oscillatory motion are given, and their properties, independent of the spin of the black holes and the angular momentum and tension of the string loops, are determined. It is shown that the radial profiles differ substantially from those corresponding to the radial and vertical frequencies of the geodetical epicyclic motion; however, they have the same mass scaling and their magnitude is of the same order. Therefore, we are able to demonstrate that, assuming the relevance of resonant phenomena of radial and vertical string-loop oscillations at their frequency ratio $3:2$, the oscillatory frequencies of string loops can be related to the frequencies of the twin high-frequency quasiperiodic oscillations (HF QPOs) observed in the microquasars GRS $1915+105$, XTE $1550-564$, GRO $1655-40$. We can conclude that oscillating current-carrying string loops have to be considered as one of the possible explanations of the HF QPOs occurring in the field of compact objects.

We show that it is not possible to UV complete certain low-energy effective theories with spontaneously broken spacetime symmetries by embedding them into linear sigma models, that is, by adding “radial” modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform nonlinearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of spacetime and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.

A new general class of solutions of ungauged four-dimensional supergravity, in one-to-one correspondence with spherically symmetric, static black-hole solutions and Lifshitz solutions with hyperscaling violation is studied. The causal structure of the space-time is then elucidated.

The flux singularity that arises for branes in oppositely charged fluxes is a widely discussed issue and in this paper the problem is investigated further. New AdS world volume (anti-)M2-brane solutions are constructed using space-filling branes placed in fluxes of opposite dissolved charge that is opposite to that of the brane. A topological obstruction is derived to show how the singularity develops during localization of this solution and any similarly constructed solution. Furthermore it is shown that it is not possible to hide the singularity behind a horizon, which would have given credence to an M theory resolution.

We show that a static spherically symmetric black hole, in a generic theory of gravity with generic matter fields, has a two-dimensional Lorentz symmetry.

We consider the retarded solution to the scalar, electromagnetic, and linearized gravitational field equations in Minkowski spacetime, with source given by a particle moving on a null geodesic. In the scalar case and in the Lorenz gauge in the electromagnetic and gravitational cases, the retarded integral over the infinite past of the source does not converge as a distribution, so we cut off the null source suitably at a finite time $t_0$ and then consider two different limits: (i) the limit as the observation point goes to null infinity at fixed $t_0$, from which the “$1/r$” part of the fields can be extracted and (ii) the limit $t_0\to -\infty$ at fixed “observation point.” The limit (i) gives rise to a “velocity kick” on distant test particles in the scalar and electromagnetic cases, and it gives rise to a “memory effect” (i.e., a permanent change in relative separation of two test particles) in the linearized gravitational case, in agreement with previous analyses. As already noted, the second limit does not exist in the scalar case or for the Lorenz gauge vector potential and Lorenz gauge metric perturbation in the electromagnetic and linearized gravitational cases. However, in the electromagnetic case, we obtain a well-defined distributional limit for the electromagnetic field strength, and in the linearized gravitational case, we obtain a well-defined distributional limit for the linearized Riemann tensor. In the gravitational case, this limit agrees with the Aichelberg-Sexl solution. There is no memory effect associated with this limiting solution. This strongly suggests that the memory effect—including nonlinear memory effect of Christodoulou—should not be interpreted as arising simply from the passage of (effective) null stress energy to null infinity but rather as arising from a “burst of radiation” associated with the creation of the null stress energy [as in case (i) above] or, more generally, with radiation present in the spacetime that was not “produced” by the null stress energy.

The construction of a generic parametrization of spinning geometries that can be matched continuously to the Kerr metric is an important open problem in general relativity. Its resolution is of more than academic interest, as it allows us to parametrize and quantify possible deviations from the no-hair theorem. Various approaches to the problem have been proposed, all with their own (severe) limitations. Here we discuss the metric recently proposed by Johannsen and Psaltis, showing that (i) the original metric describes only corrections that preserve the horizon area-mass relation of nonspinning geometries, (ii) this unnecessary restriction can be relaxed by introducing a new parameter that in fact dominates in both the weak-field and strong-field regimes, (iii) within this framework, we construct the most generic spinning black-hole geometry that contains twice as many (infinite) parameters as the original metric, and (iv) in the strong-field regime, all parameters are (roughly) equally important. This fact introduces a severe degeneracy problem in the case of highly spinning black holes. Our results suggest that using parametrizations that affect only the quadrupole moment of the Kerr geometry is problematic, because higher-order multipoles can be equally relevant for highly spinning objects. Finally, we prove that even our generalization fails to describe the few known spinning black-hole metrics in modified gravity.

A six-dimensional standing-wave braneworld model has been constructed. It consists of an anisotropic four-brane generated by standing gravitational waves whose source is normal matter. In this model, the compact (on-brane) dimension is assumed to be sufficiently small in order to describe our Universe (hybrid compactification). The bulk geometry is nonstatic, unlike most of the braneworld models in the literature. The principal feature of this model is the fact that the source is not a phantomlike scalar field, as the original standing-wave model that was proposed in five dimensions and its six-dimensional extension recently proposed in the literature. Here, it was obtained a solution in the presence of normal matter what assures that the model is stable. Also, our model is the first standing-wave brane model in the literature that can be applied successfully to the hierarchy problem. Additionally, we have shown that the zero mode for the scalar and fermionic fields is localized around the brane. In particular, for the scalar field we show that it is localized on the brane, regardless of whether the warp factor is decreasing or increasing. This is in contrast to the case of the local stringlike defect, where the scalar field is localized for a decreasing warp factor only.

We present the dynamics of rotating Bose condensate Galactic dark matter halos, made of an ultralight spinless boson. We restrict to the case of adding axisymmetric rigid rotation to initially spherically symmetric structures and show there are three regimes: (i) small angular momentum, which basically retains the drawbacks of spherically symmetric halos related to compactness and failure at explaining Galactic rotation curves; (ii) an intermediate range of values of angular momentum that allow the existence of long-lived structures with acceptable rotation curve profiles; and (iii) high angular momentum, in which the structure is dispersed away by rotation. We also present in detail the new code used to solve the Gross–Pitaevskii Poisson system of equations in three dimensions.

We consider massive $\lambda {\varphi }^4$ theory in de Sitter background. The mass of the scalar field $\varphi$ is chosen small enough, such that the amplification of superhorizon momentum modes leads to a significant enhancement of infrared correlations, but large enough such that perturbation theory remains valid. Using the closed-time-path approach, we calculate the infrared corrections to the two-point function of $\varphi$ to two-loop order. To this approximation, we find agreement with the correlation found using stochastic methods. When breaking the results down to individual Feynman diagrams obtained by the two different methods, we observe that these agree as well.

A logamediate inflationary model in the presence of the tachyon scalar field will be studied. Considering slow-roll inflation, the equations of motion of the Universe and the tachyon field will be derived. In the context of perturbation theory, some important perturbation parameters will be obtained and using numerical calculations, the consistency of our model with observational data will be illustrated.

We report on a detailed numerical study of the evolution of semilocal string networks, based on the largest and most accurate field theory simulations of these objects to date. We focus on the large-scale network properties, confirming earlier indications (coming from smaller simulations) that linear scaling is the attractor solution for the entire parameter space of initial conditions that we are able to probe. We also provide a brief comparison of our numerical results with the predictions of a previously developed one-scale model for the overall evolution of these networks. Two subsequent papers will discuss in more detail the analytic modeling of the semilocal segment populations as well as optimized numerical diagnostics.

The detection of gravitational waves and the extraction of physical information from them requires the prediction of accurate waveforms to be used in template banks. For that purpose, the accuracy of effective-one-body (EOB) waveforms has been improved over the last years by calibrating them to numerical-relativity (NR) waveforms. So far, the calibration has employed a handful of NR waveforms with a total length of $\sim 30$ cycles, the length being limited by the computational cost of NR simulations. Here, we address the outstanding problem of the stability of the EOB calibration with respect to the length of NR waveforms. Performing calibration studies against NR waveforms of nonspinning black-hole binaries with mass ratios 1, 1.5, 5 and 8, and with a total length of $\sim 60$ cycles, we find that EOB waveforms calibrated against either 30 or 60 cycles will be indistinguishable by the advanced detectors Laser Interferometric Gravitational-wave Observatory (LIGO) and Virgo when the signal-to-noise ratio (SNR) is below 110. When extrapolating to a very large number of cycles, using very conservative assumptions, we can conclude that state-of-the-art nonspinning EOB waveforms of any length are sufficiently accurate for parameter estimation with advanced detectors when the SNR is below 20, the mass ratio is below 5 and the total mass is above $20M_{\odot }$. The results are not conclusive for the entire parameter space because of current NR errors.

In a recent series of papers, we have shown that theories with scalar fields coupled to gravity (e.g., the standard model) can be lifted to a Weyl-invariant equivalent theory in which it is possible to unambiguously trace the classical cosmological evolution through the transition from big crunch to big bang. The key was identifying a sufficient number of finite, Weyl-invariant conserved quantities to uniquely match the fundamental cosmological degrees of freedom across the transition. In doing so we had to account for the well-known fact that many Weyl-invariant quantities diverge at the crunch and bang. Recently, some authors rediscovered a few of these divergences and concluded based on their existence alone that the theories cannot be geodesically complete. In this paper, we show that this conclusion is invalid. Using conserved quantities we explicitly construct the complete set of geodesics and show that they pass continuously through the big crunch-big bang transition.

It has been previously shown numerically that the expectation value of the magnetic Wilson loop at the initial time of a heavy-ion collision exhibits area law scaling. This was obtained for a classical non-Abelian gauge field in the forward light cone and for loops of area $A\gtrsim 2/Q_s^2$. Here, we present an analytic calculation of the spatial Wilson loop in the classical field of a collision within perturbation theory. It corresponds to a diagram with two sources, for both projectile and target, whose field is evaluated at second order in the gauge potential. The leading nontrivial contribution to the magnetic loop in perturbation theory is proportional to the square of its area.

We analyze the behavior of several renormalization group functions at infrared fixed points for $SU(N)$ gauge theories with fermions in the fundamental and two-indexed representations. This includes the beta function of the gauge coupling, the anomalous dimension of the gauge parameter and the anomalous dimension of the mass. The scheme in which the analysis is performed is the minimal momentum subtraction scheme through third-loop order. Because of the fact that scheme dependence is inevitable once the perturbation theory is truncated we compare to previous identical studies done in the minimal subtraction scheme and the modified regularization invariant scheme. We find only mild to moderate scheme dependence.

In the one-photon exchange approximation we discuss questions related to the interpretation of unexpected results of the JLab polarization experiments to measure the Sachs form factors ratio $G_E/G_M$ in the region $1.0\le Q^2\le 8.5{\mathrm{GeV}}^2$. For this purpose, we developed an approach which essentially is a generalization of the constituent-counting rules of the perturbative QCD (pQCD) for the case of massive quarks. We assume that at the lower boundary of the considered region the hard-scattering mechanism of pQCD is realized. Within the framework of the developed approach we calculated the hard kernel of the proton current matrix elements $J_p^{\pm \delta ,\delta }$ for the full set of spin combinations corresponding to the number of the spin-flipped quarks, which contribute to the proton transition without spin-flip ($J_p^{\delta ,\delta }$) and with spin-flip ($J_p^{-\delta ,\delta }$). This allows us to state that (i) around the lower boundary of the considered region, the leading scaling behavior of the Sachs form factors has the form $G_E,G_M\sim 1/Q^6$, (ii) the dipole dependence ($G_E,G_M\sim 1/Q^4$) is realized in the asymptotic regime of pQCD when $\tau \gg 1$ ($\tau =Q^2/4M^2$) in the case when the quark transitions with spin-flip dominate, (iii) the asymptotic regime of pQCD in the JLab experiments has not yet been achieved, and (iv) the linear decrease of the ratio $G_E/G_M$ at $\tau <1$ is due to additional contributions to $J_p^{\delta ,\delta }$ by spin-flip transitions of two quarks and an additional contribution to $J_p^{-\delta ,\delta }$ by spin-flip transitions of three quarks.

We present an effective model, which is an extension of the usual linear sigma model, that contains a low energy multiplet for every hadronic particle type. These multiplets are a scalar nonet, a pseudoscalar nonet, a vector nonet, an axial-vector nonet, a baryon octet and a baryon decuplet. Tree-level baryon masses and possible two-body decuplet decays are calculated. The baryon masses are generated through spontaneous symmetry breaking. The calculated quantities are used to determine the model parameters through a multiparametric minimalization process, which compares the calculated physical quantities with their experimental values. We found that the calculated quantities are in good agreement with the experimental data.

The LHC has placed stringent limits on superpartner masses, in conflict with naturalness. $R$-parity violation is one of the few scenarios that allows for the reduction of these limits and is thus worth significant exploration at the LHC. We demonstrate that if the $R$-parity-violating operator $UDD$ is used, we generically expect all supersymmetric events at the LHC to have displaced vertices. If a squark is the lightest supersymmetric particle (LSP), it will have a short displaced vertex. If any other particle is the LSP, the displaced vertex is naturally expected to be quite long, possibly even outside the detectors. These scenarios are already constrained by existing searches for missing energy. This arises because this operator efficiently washes out the baryon asymmetry in the early Universe, unless the squarks are heavy and the coupling is small. Avoiding displaced vertices is possible, but requires baryogenesis below the weak scale. Thus, for example, the use of sphalerons in baryogenesis does not avoid the requirement of displaced vertices. This motivates searching for hadronic displaced vertices at the LHC with decay lengths anywhere from tens of microns to meters.

In this paper, we estimate the size of twist-3 corrections to the deeply virtual meson production in neutrino interactions due to the chiral odd transversity generalized parton distribution (GPD). We conclude that in contrast to pion electroproduction, in neutrino-induced reactions, these corrections are small. This happens due to the large contribution of unpolarized GPDs $H,E$ to the leading-twist amplitude in neutrino production. We provide a computational code, which can be used for evaluation of the cross sections accounting for these twist-3 corrections with various GPD models. Our results are particularly relevant for analyses of the pion and kaon production in the MINERvA experiment at Fermilab.