At finite temperature and in nonequilibrium environments we have to resum perturbation theory to avoid infrared divergences. Since resummation shuffles the perturbative orders, renormalizability is a nontrivial issue. In this paper we demonstrate that one can modify any type of resummations—even if it is momentum dependent, or it resums higher point functions—in a way that it is renormalizable with the usual zero temperature counterterms. To achieve this goal we reformulate resummation in form of a renormalization scheme. We apply this technique to perform a 2PI resummation in the six dimensional cubic scalar model in equilibrium.

Previous evaluations of long range one-photon and one-graviton-loop corrections to the energy-momentum tensor and the metric tensor describing spacetime in the vicinity of massive spinless and spin $1/2$ systems have been extended to particles with unit spin and speculations are confirmed concerning universal properties of such forms.

We consider here scalar and electromagnetic perturbations for the Vaidya metric in double-null coordinates. Such an approach allows one to go a step further in the analysis of quasinormal modes for time-dependent spacetimes. Some recent results are refined, and a new nonstationary behavior corresponding to some sort of inertia for quasinormal modes is identified. Our conclusions can enlighten some aspects of the wave scattering by black holes undergoing some mass accretion processes.

We calculate the Meissner screening mass of gluons 4–7 in two-flavor quark matter at nonzero temperature. To this end, we study the effective potential of the $2\mathrm{SC}/\mathrm{g}2\mathrm{SC}$ phases including a vector condensate $⟨g{A}_z^6⟩$ and calculate the Meissner mass from the potential curvature with respect to $⟨g{A}_z^6⟩$. We find that the Meissner mass becomes real at the critical temperature which is about the half of the chemical potential mismatch. The phase diagram of the neutral two-flavor color superconductor is presented in the plane of temperature and coupling strength. We indicate the unstable region for gluons 4–7 on the phase diagram.

We reduce M theory on a $G_2$ orbifold with codimension four singularities, taking explicitly into account the additional gauge fields at the singularities. As a starting point, we use 11-dimensional supergravity coupled to seven-dimensional super-Yang-Mills theory, as derived in a previous paper. The resulting four-dimensional theory has $\mathcal{N}=1$ supersymmetry with non-Abelian $\mathcal{N}=4$ gauge theory subsectors. We present explicit formulas for the Kähler potential, gauge-kinetic function and superpotential. In the four-dimensional theory, blowing up of the orbifold is described by a Higgs effect induced by continuation along $D$-flat directions. Using this interpretation, we show that our results are consistent with the corresponding ones obtained for smooth $G_2$ spaces. In addition, we consider the effects of switching on flux and Wilson lines on singular loci of the $G_2$ space, and we discuss the relation to $\mathcal{N}=4$ super-Yang-Mills theory.

We present numerical results from three-dimensional evolutions of scalar perturbations of Kerr black holes. Our simulations make use of a high-order accurate multiblock code which naturally allows for adapted grids and smooth inner (excision) and outer boundaries. We focus on the quasinormal ringing phase, presenting a systematic method for extraction of the quasinormal mode frequencies and amplitudes and comparing our results against perturbation theory. The detection of a single mode in a ringdown waveform allows for a measurement of the mass and spin of a black hole; a multimode detection would allow a test of the Kerr nature of the source. Since the possibility of a multimode detection depends on the relative mode amplitude, we study this topic in some detail. The amplitude of each mode depends exponentially on the starting time of the quasinormal regime, which is not defined unambiguously. We show that this time-shift problem can be circumvented by looking at appropriately chosen relative mode amplitudes. From our simulations we extract the quasinormal frequencies and the relative and absolute amplitudes of corotating and counterrotating modes (including overtones in the corotating case). We study the dependence of these amplitudes on the shape of the initial perturbation, the angular dependence of the mode, and the black hole spin, comparing against results from perturbation theory in the so-called asymptotic approximation. We also compare the quasinormal frequencies from our numerical simulations with predictions from perturbation theory, finding excellent agreement. For rapidly rotating black holes (of spin $j=0.98$) we can extract the quasinormal frequencies of not only the fundamental mode, but also of the first two overtones. Finally we study under what conditions the relative amplitude between given pairs of modes gets maximally excited and present a quantitative analysis of rotational mode-mode coupling. The main conclusions and techniques of our analysis are quite general and, as such, should be of interest in the study of ringdown gravitational waves produced by astrophysical gravitational wave sources.

Encouraged by the latest SNO results, we consider the lepton mixing matrix in the approximation that the ${\nu }_2$ mass eigenstate is trimaximally (democratically) mixed. This suggests a new parameterization of the remaining mixing degrees of freedom, which eschews mixing angles, dealing instead, directly with the complex parameter $U_{e3}$ of the mixing matrix. Unitarity triangles then take a particularly simple form, which we hope will facilitate comparison with experiment.

$f(R)$-theories of gravity are reviewed in the context of the so called gravitational baryogenesis. The latter is a mechanism for generating the baryon asymmetry in the Universe, and relies on the coupling between the Ricci scalar curvature $R$ and the baryon current. Gravity Lagrangians of the form $\mathcal{L}(R)\sim R^n$, where $n$ differs from 1 (the case of the General Relativity) only for tiny deviations of a few percent, are consistent with the current bounds on the observed baryon asymmetry.

The computation of the one-loop effective action in a radially symmetric background can be reduced to a sum over partial-wave contributions, each of which is the logarithm of an appropriate one-dimensional radial determinant. While these individual radial determinants can be evaluated simply and efficiently using the Gel’fand-Yaglom method, the sum over all partial-wave contributions diverges. A renormalization procedure is needed to unambiguously define the finite renormalized effective action. Here we use a combination of the Schwinger proper-time method, and a resummed uniform DeWitt expansion. This provides a more elegant technique for extracting the large partial-wave contribution, compared to the higher-order radial WKB approach which had been used in previous work. We illustrate the general method with a complete analysis of the scalar one-loop effective action in a class of radially separable SU(2) Yang-Mills background fields. We also show that this method can be applied to the case where the background gauge fields have asymptotic limits appropriate to uniform field strengths, such as, for example, in the Minkowski solution, which describes an instanton immersed in a constant background. Detailed numerical results will be presented in a sequel.

We examine the Casimir effect for a perfectly conducting cylinder of elliptical section, taking as reference the known case of circular section. The zero-point energy of this system is evaluated by the mode summation method, using the ellipticity as a perturbation parameter. Mathieu function techniques are applied.

If there is a family-independent extra $U(1)$ gauge symmetry broken at low energies, then it may be possible from the charges of the known quarks and leptons under this $U(1)$ to make inferences about how much gauge unification occurs at high scales and about the unification group. (For instance, there are certain observed properties of an extra $U(1{)}^{\prime }$ that would be inconsistent with unification in four dimensions at high scales.) A general analysis is presented. Two criteria used in this analysis are (1) the degree to which the generator of the extra $U(1)$ mixes with hypercharge, and (2) the ratio of the extra $U(1)$ charge of the “10” and the “$\overline{5}$” of quarks and leptons.

We investigate the two-dimensional behavior of gravity coupled to a dynamical unit timelike vector field, i.e. “Einstein-aether theory.” The classical solutions of this theory in two dimensions depend on one coupling constant. When this coupling is positive the only solutions are (i) flat spacetime with constant aether, (ii) de Sitter or anti-de Sitter spacetimes with a uniformly accelerated unit vector invariant under a two-dimensional subgroup of $SO(2,1)$ generated by a boost and a null rotation, and (iii) a nonconstant curvature spacetime that has no Killing symmetries and contains singularities. In this case the sign of the curvature is determined by whether the coupling is less or greater than one. When instead the coupling is negative only solutions (i) and (iii) are present. This classical study of the behavior of Einstein-aether theory in $1+1$ dimensions may provide a starting point for further investigations into semiclassical and fully quantum toy models of quantum gravity with a dynamical preferred frame.

We compute the exact gravitational quasinormal frequencies for massless topological black holes in $d$-dimensional anti-de Sitter space. Using the gauge invariant formalism for gravitational perturbations derived by Kodama and Ishibashi, we show that in all cases the scalar, vector, and tensor modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of the gravitational quasinormal frequencies.

We show that the hierarchy between the Planck and the weak scales can follow from the tendency of gravitons and fermions to localize at different edges of a thick double wall embedded in an ${\mathrm{AdS}}_5$ spacetime without reflection symmetry. This double wall is a stable BPS thick-wall solution with two subwalls located at its edges; fermions are coupled to the scalar field through Yukawa interactions, but the lack of reflection symmetry forces them to be localized in one of the subwalls. We show that the graviton zero-mode wave function is suppressed in the fermion edge by an exponential function of the distance between the subwalls, and that the massive modes decouple so that Newtonian gravity is recuperated.

We resolve discrepancies in previous analyses of the flow of collisionless dark matter particles in the Sun’s gravitational field. We determine the phase-space distribution of the flow both numerically, tracing particle trajectories back in time, and analytically, providing a simple correct relation between the velocity of particles at infinity and at the Earth. We use our results to produce sky maps of the distribution of arrival directions of dark matter particles on Earth at various times of the year. We assume various Maxwellian velocity distributions at infinity describing the standard dark halo and streams of dark matter. We illustrate the formation of a ring, analogous to the Einstein ring, when the Earth is directly downstream of the Sun.

We study the prospects for extracting cosmological and astrophysical parameters from the low radio frequency 21-cm background due to the spin-flip transition of neutral hydrogen during and prior to the reionization of the Universe. We make use of the angular power spectrum of 21-cm anisotropies, which exists due to inhomogeneities in the neutral hydrogen density field, the gas temperature field, the gas velocity field, and the spatial distribution of the Lyman-$\alpha$ intensity field associated with first luminous sources that emit UV photons. We extract parameters that describe both the underlying mass power spectrum and the global cosmology, as well as a set of simplified astrophysical parameters that connect fluctuations in the dark matter to those that govern 21-cm fluctuations. We also marginalize over a model for the foregrounds at low radio frequencies. In this general description, we find large degeneracies between cosmological parameters and the astrophysical parameters, though such degeneracies are reduced when strong assumptions are made with respect to the spin temperature relative to the cosmic microwave background (CMB) temperature or when complicated sources of anisotropy in the brightness temperature are ignored. Some of the degeneracies between cosmological and astrophysical parameters are broken when 21-cm anisotropy measurements are combined with information from the CMB, such as the temperature and the polarization measurements with Planck. While the overall improvement on the cosmological parameter estimates is not significant when measurements from first-generation interferometers are combined with Planck, such a combination can measure astrophysical parameters such as the ionization fraction in several redshift bins with reasonable accuracy.

The opening of a new $S$-wave threshold is frequently accompanied by an abrupt dip in the magnitude of an amplitude for an already-open channel. One familiar example is the behavior of the $I=0$ $S$-wave $\pi \pi$ scattering amplitude at $K\overline{K}$ threshold. Numerous other examples of this phenomenon in recent data are noted, and a unified description of the underlying dynamics is sought.

We investigate the leading-twist light-cone distribution amplitudes for the pion and kaon based on the gauge-invariant nonlocal chiral quark model from the instanton vacuum in the presence of external axial-vector currents. We find that the nonlocal contribution from the gauge invariance has much effects on the pion distribution amplitudes, while it changes mildly the kaon ones. We also study the Gegenbauer moments of the distribution amplitudes and compare them with the empirical analysis of the CLEO data.