In planar (baby) Skyrme systems, there may be extended linear structures which resemble either domain walls or chains of skyrmions, depending on the choice of potential and boundary conditions. We show that systems with a single vacuum, for example, with potential $V=1-{\varphi }_3$, admit chain solutions, whereas walls are ruled out by the uniqueness of the vacuum. On the other hand, in double-vacuum systems such as $V=\frac{1}{2}(1-{\varphi }_3^2)$, one has stable wall solutions, but there are no stable chains; the walls may be viewed as the primary objects in such systems, with skyrmions being made out of them.

We calculate Lorentz-invariant and gauge-invariant quantities characterizing the product $\sum _a{D}_R(T^a)F_{\mu \nu }^a$, where $D_R(T^a)$ denotes the matrix for the generator $T^a$ in the representation $R=\mathrm{\text{fundamental}}$ and adjoint, for color SU(3). We also present analogous results for an SU(2) gauge theory.

We modify a stellar structure code to estimate the effect upon the main sequence of the accretion of weakly-interacting dark matter onto stars and its subsequent annihilation. The effect upon the stars depends upon whether the energy generation rate from dark matter annihilation is large enough to shut off the nuclear burning in the star. Main sequence weakly-interacting massive particles (WIMP) burners look much like proto-stars moving on the Hayashi track, although they are in principle completely stable. We make some brief comments about where such stars could be found, how they might be observed and more detailed simulations which are currently in progress. Finally we comment on whether or not it is possible to link the paradoxically hot, young stars found at the galactic center with WIMP burners.

We give a higher-spin generalization of the anomaly method for the Hawking radiation from black holes. In the paper [S. Iso, T. Morita, and H. Umetsu, arXiv:0710.0453.] higher-spin generalizations of the gauge (and gravitational) anomalies in $d=2$ were obtained. By applying these anomalies to black hole physics, we derive the higher moments of the Hawking fluxes. We also give a higher-spin generalization of the trace anomaly method by Christensen and Fulling [S. Christensen and S. Fulling, Phys. Rev. D 15, 2088 (1977).].

Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and unambiguous criterion of the adiabatic approximation. This is illustrated for the model of Marzlin and Sanders [Phys. Rev. Lett. 93, 160408 (2004)] and a model related to the geometric phase which can be exactly diagonalized in the present sense.

A multiple scattering formulation is used to calculate the force, arising from fluctuating scalar fields, between distinct bodies described by $\delta$-function potentials, so-called semitransparent bodies. (In the limit of strong coupling, a semitransparent boundary becomes a Dirichlet one.) We obtain expressions for the Casimir energies between disjoint parallel semitransparent cylinders and between disjoint semitransparent spheres. In the limit of weak coupling, we derive power series expansions for the energy, which can be exactly summed, so that explicit, very simple, closed-form expressions are obtained in both cases. The proximity force theorem holds when the objects are almost touching, but is subject to large corrections as the bodies are moved farther apart.

Our previously developed calculational method (the partial-wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be particularly effective when it is used in conjunction with a systematic WKB series for the large partial-wave contribution to the effective action. By comparing these numerically exact calculations against the predictions based on the large-mass expansion and derivative expansion, we discuss the validity ranges of the latter approximation methods.

The 4-dimensional model with topological mass generation that has recently been presented by Dvali, Jackiw, and Pi [G. Dvali, R. Jackiw, and S.-Y. Pi, Phys. Rev. Lett. 96, 081602 (2006)] is generalized to any even number of dimensions. As in the 4-dimensional model, the $2n$-dimensional model describes a mass-generation phenomenon due to the presence of the chiral anomaly. In addition to this model, new $2n$-dimensional models with topological mass generation are proposed, in which a Stückelberg-type mass term plays a crucial role in the mass generation. The mass generation of a pseudoscalar field such as the ${\eta }^{\prime }$ meson is discussed within this framework.

The holographic basis is a novel tool which allows for a quantitative description of elementary/composite mixing in holographic duals of warped models. We apply this tool to bulk fermions in a slice of ${\mathrm{AdS}}_5$ and determine the precise admixture of elementary source field and composite resonances forming the standard model fermions. In particular, for the phenomenologically important case of an IR localized right-handed top quark, we show that the massless eigenstate is approximately a $50/50$ elementary-composite admixture. We also translate, in a simple yet quantitative manner, several of the phenomenological successes enjoyed by warped models to the language of partial compositeness.

The Rainich’s program of describing metrics induced by pure electromagnetic fields is implemented in a simpler way by using the Ernst formalism and increasing the symmetry of spacetime. Stationary metrics possessing one, two or three Killing vectors are studied and classified. Three branches of solutions exist. Electromagnetically induced mass terms appear in two of them, including a class of solutions in harmonic functions. The static subcase is discussed too. Relations to other well-known electrovacuum metrics are elucidated.

A thick brane in six dimensions is constructed using two scalar fields. The field equations for 6D gravity plus the scalar fields are solved numerically. This thick brane solution shares some features with previously studied analytic solutions, but has the advantage that the energy-momentum tensor which forms the thick brane comes from the scalar fields rather than being put in by hand. Additionally the scalar fields which form the brane also provide a universal, nongravitational trapping mechanism for test fields of various spins.

We expand previous work on an inverse approach to Einstein field equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class $B_1$. Although restricted, these spacetimes include many exact solutions of interest to compact object studies and to cosmological models studies. The question explored here is as follows: given a spacetime metric, what fluid flow (timelike congruence), if any, could generate the spacetime via Einstein’s equations? We calculate the flow from the condition of a vanishing anisotropic stress tensor and give results in terms of the metric functions in the three canonical types of coordinates. A condition for perfect fluid sources is also provided. The framework developed is algorithmic and suited for the study and validation of exact solutions using computer algebra systems. The framework can be applied to solutions in comoving and noncomoving frames of reference, and examples in different types of coordinates are worked out.

We consider the scattering of a low-frequency gravitational wave by a massive compact body in vacuum. We apply partial-wave methods to compute amplitudes for the helicity-conserving and helicity-reversing contributions to the cross section, accurate to first order in $M\omega$. Contrary to previous claims, we find that the partial-wave cross section agrees with the cross section derived via perturbation-theory methods.

Most cosmological parameters are expected to change significantly only on cosmological time scales, but given the large amount of information contained within the cosmic microwave background (CMB) sky, we can expect that changes in the CMB should be observable on much shorter time scales. Here we quantify this expectation, examining the detectability of the dominant effects on short time scales. We find that an ideal future experiment with currently achievable sensitivity could detect the changing dipole due to our galactic motion in about 5 years, but that it would take around 4000 years to detect a change in the higher order multipoles.

We study numerically a class of nontopological solitons, the $Q$-balls, arising in a supersymmetric extension of the standard model with low-energy, gauge-mediated symmetry breaking. Taking into account the exact form of the supersymmetric potential giving rise to $Q$-balls, we find that there is a lower limit on the value of the charge $Q$ in order to make them classically stable: $Q\gtrsim 5\times {10}^2{Q}_{\mathrm{cr}}$, where $Q_{\mathrm{cr}}$ is constant depending on the parameters defining the potential and can be in the range $1\lesssim Q_{\mathrm{cr}}\lesssim {10}^{8÷16}$. If $Q$ is the baryon number, stability with respect to the decay into protons requires $Q\gtrsim {10}^{17}{Q}_{\mathrm{cr}}$, while if the gravitino mass is greater then $m_{3/2}\gtrsim 61\mathrm{MeV}$, no stable gauge-mediation supersymmetric $Q$-balls exist. Finally, we find that energy and radius of $Q$-balls can be parametrized as $E\sim {\xi }_E{Q}^{3/4}$ and $R\sim {\xi }_R{Q}^{1/4}$, where ${\xi }_E$ and ${\xi }_R$ are slowly varying functions of the charge.

We propose a numerical test of fundamental physics based on the complexity measure of a general set of functions, which is directly related to the Kolmogorov (or algorithmic) complexity studied in mathematics and computer science. The analysis can be carried out for any scientific experiment and might lead to a better understanding of the underlying theory. From a cosmological perspective, the anthropic description of fundamental constants can be explicitly tested by our procedure. We perform a simple numerical search by analyzing two fundamental constants: the weak coupling constant and the Weinberg angle, and find that their values are rather atypical.

We consider the evolution of the vacuum energy in the Dvali-Gabadadze-Porrati (DGP) model according to the holographic principle under the assumption that the relation linking the IR and UV cutoffs still holds in this scenario. The model is studied when the IR cutoff is chosen to be the Hubble scale $H^{-1}$, the particle horizon $R_{\mathrm{ph}}$, and the future event horizon $R_{\mathrm{eh}}$, respectively. The two branches of the DGP model are also taken into account. Through numerical analysis, we find that in the cases of $H^{-1}$ in the ($+$) branch and $R_{\mathrm{eh}}$ in both branches, the vacuum energy can play the role of dark energy. Moreover, when considering the combination of the vacuum energy and the $5\mathrm{D}$ gravity effect in both branches, the equation of state of the effective dark energy may cross $-1$, which may lead to the big rip singularity. Besides, we constrain the model with the Type Ia supernovae and baryon oscillation data and find that our model is consistent with current data within $1\sigma$, and that the observations prefer either a pure holographic dark energy or a pure DGP model.

The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binary-inspiral waveforms; and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond-Fisher-matrix terms in the $1/\mathrm{SNR}$ expansions for the expected parameter accuracies.

We calculate the matrix elements of the gluonic contributions to the energy-momentum tensor for a pion of mass $600<M_{\pi }<1100\mathrm{MeV}$ in quenched lattice QCD. We find that gluons contribute $(37\pm 8\pm 12)\%$ of the pion’s light-cone momentum. The bare matrix elements corresponding to the trace anomaly contribution to the pion mass are also obtained. The discretizations of the energy-momentum tensor we use have other promising applications, ranging from calculating the origin of hadron spin to QCD thermodynamics.