A bosonic string coupled to the generalized Chern-Simons theory in $3+1\mathrm{D}$ acquires a magnetic field along itself, when it is closed, and a topological charge at its extremity, when it is open. We construct the creation operators for the full quantum field states associated with these strings and determine the dual algebra satisfied by them. We show that the creation operator for the composite state of a quantum closed bosonic string, bearing a magnetic flux, and a topologically charged open bosonic string, possesses generalized statistics. The relation of our results with previous approaches to the problem is also established.

We suggest a paradigm that might allow for a nonanthropic solution to the cosmic coincidence problem of why the density of vacuum energy and matter are nearly equal today. The fact that the half life of uranium 238 is near to the age of the solar system is not considered a coincidence since there are many nuclides with a wide range of half lives implying that there is likely to be some nuclide with a half life near to any given time scale. Likewise it may be that the vacuum field energy causing the universal acceleration today is just one of a large ensemble of scalar field energies, which have dominated the Universe in the past and then faded away. Predictions of the idea include the following: the current density of vacuum energy is decreasing, the ratio of vacuum pressure to vacuum density, w, is changing and not equal to $-1,$ there were likely periods of vacuum domination and acceleration in the past and may be additional periods in the future, and the eventual sum of all scalar field vacuum densities may be zero.

We present the calculation of the $n_f$ contributions to the two-loop amplitude for $e^{+}{e}^{-}\to q\overline{q}g$ and give results for the full one-loop amplitude to order ${\varepsilon }^2$ in the dimensional regularization parameter. Our results agree with those recently obtained by Garland et al. The calculation makes extensive use of an efficient method based on nested sums to calculate two-loop integrals with arbitrary powers of the propagators. The use of nested sums leads in a natural way to multiple polylogarithms with simple arguments, which allow a straightforward analytic continuation.

Motivated by the conjecture that the cosmological constant problem could be solved by strong quantum effects in the infrared, we use the exact flow equation of quantum Einstein gravity to determine the renormalization group behavior of a class of nonlocal effective actions. They consist of the Einstein-Hilbert term and a general nonlinear function ${\mathcal{F}}_k\mathrm{}\left(V\right)\mathrm{}$ of the Euclidean space-time volume V. A partial differential equation governing its dependence on the scale k is derived and its fixed point is analyzed. For the more restrictive truncation of theory space where ${\mathcal{F}}_k\mathrm{}\left(V\right)\mathrm{}$ is of the form $V+V\ln V,$ ${V+V}^2,$ and $V+\sqrt{V},$ respectively, the renormalization group equations for the running couplings are solved numerically. The results are used in order to determine the k-dependent curvature of the $S^4$-type Euclidean space-times which are solutions to the effective Einstein equations, i.e., stationary points of the scale dependent effective action. For the $V+V\ln V$-invariant (discussed earlier by Taylor and Veneziano) we find that the renormalization group running enormously suppresses the value of the renormalized curvature which results from Planck-size bare parameters specified at the Planck scale. Hence one can obtain very large, almost flat universes without fine-tuning the cosmological constant.

We investigate the dynamics of a spherically symmetric vacuum on a Randall and Sundrum 3-brane world. Under certain natural conditions, the effective Einstein equations on the brane form a closed system for spherically symmetric dark radiation. We determine exact dynamical and inhomogeneous solutions, which are shown to depend on the brane cosmological constant, on the dark radiation tidal charge and on its initial energy configuration. We identify the conditions defining these solutions as singular or as globally regular. Finally, we discuss the confinement of gravity to the vicinity of the brane and show that a phase transition to a regime where gravity is not bound to the brane may occur at short distances during the collapse of positive dark energy density on a realistic de Sitter brane.

We examine, from both a qualitative and a numerical point of view, the evolution of Kantowski-Sachs cosmological models whose source is a mixture of a gas of weakly interacting massive particles (WIMP’s) and a radiative gas made up of a “tightly coupled” mixture of electrons, baryons and photons. Our analysis is valid from the end of nucleosynthesis up to the duration of radiative interactions ${(10\mathrm{}}^6\mathrm{K}>T>\mathrm{}4\mathrm{}\times {10}^3\mathrm{K}).\mathrm{}$ In this cosmic era annihilation processes are negligible, while the WIMP’s only interact gravitationally with the radiative gas and the latter behaves as a single dissipative fluid that can be studied within a hydrodynamical framework. Applying the full transport equations of extended irreversible thermodynamics, coupled with the field and balance equations, we obtain a set of governing equations that becomes an autonomous system of ordinary differential equations once the shear viscosity relaxation time ${\tau }_{\mathrm{rel}}$ is specified. Assuming that ${\tau }_{\mathrm{rel}}$ is proportional to the Hubble time, the qualitative analysis indicates that models begin in the radiation-dominated epoch close to an isotropic equilibrium point (saddle). We show how the form of ${\tau }_{\mathrm{rel}}$ governs the relaxation time scale of the models towards an equilibrium photon entropy, leading to “near-Eckart” and transient regimes associated with “abrupt” and “smooth” relaxation processes, respectively. Assuming the WIMP particle to be a supersymmetric neutralino with a mass $m_{\mathrm{w}}\sim 100\mathrm{GeV},$ the numerical analysis reveals that a physically plausible evolution, compatible with a stable equilibrium state and with observed bounds on CMB anisotropies and neutralino abundance, is only possible for models characterized by initial conditions associated with nearly zero spatial curvature and total initial energy density close to unity. An expression for the relaxation time, complying with physical requirements, is obtained in terms of the dynamical equations. It is also shown that the “truncated” transport equation does not give rise to acceptable physics.

We present a new hydrocode based on spectral methods using spherical coordinates. The first version of this code aims at studying time evolution of inertial modes in slowly rotating neutron stars. In this paper, we introduce the anelastic approximation, developed in atmospheric physics, using the mass conservation equation to discard acoustic waves. We describe our algorithms and some tests of the linear version of the code, and also some preliminary linear results. We show, in the Newtonian framework with a differentially rotating background, as in the relativistic case with the strong Cowling approximation, that the main part of the velocity quickly concentrates near the equator of the star. Thus, our time evolution approach gives results analogous to those obtained by Karino, Yoshida, and Eriguchi [Phys. Rev. D 64, 024003 (2001)] within a calculation of eigenvectors. Furthermore, in agreement with the work of Lockitch, Andersson, and Friedman [Phys. Rev. D 63, 024019 (2001)], we found that the velocity seems to always get a nonvanishing polar part.

We discuss the generalization to global gauge anomalies of the familiar procedure for the cancellation of local gauge anomalies in effective theories of spontaneously broken symmetries. We illustrate this mechanism in a recently proposed six-dimensional extension of the standard model.

We study a generalization of the group of loops that is based on sets of signed points, instead of paths or loops. This geometrical setting incorporates the kinematical constraints of the sigma model, inasmuch as the group of loops does with Bianchi identities of Yang-Mills theories. We employ an Abelian version of this construction to quantize the self-dual model, which allows us to relate this theory with that of a massless scalar field obeying nontrivial boundary conditions.

A family of $\mathrm{SO}\left(10\right)\mathrm{}$ symmetric instanton solutions in type IIB supergravity is developed. The instanton of least action is a candidate for the low-energy, semiclassical approximation to the $\mathrm{D}=-1$ brane. Unlike the solution of Gibbons, Green, and Perry, this admits an interpretation as a tunneling amplitude between perturbatively degenerate asymptotic states, but with an action twice that found previously. A number of associated issues are discussed such as the relation between the magnetic and electric pictures, an inversion symmetry of the dilaton and the metric, the $R\times S^9$ topology of the background, and some properties of the solution in an “instanton frame” corresponding to a Lagrangian in which the dilaton’s kinetic energy vanishes.

We investigate the presence of domain walls in models described by three real scalar fields. We search for stable defect structures which minimize the energy of the static field configurations. We work out explict orbits in field space and find several analytical solutions in all Bogomol’nyi-Prasad-Sommerfield (BPS) sectors, some of them presenting internal structure such as the appearence of defects inside defects. We point out explicit applications in high energy physics, and in other branches of nonlinear science.

It is shown that ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ supergravity has hitherto unnoticed supersymmetric properties that are related to a hidden 12-dimensional structure. The totality of the ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ supergravity Kaluza-Klein towers is given by a single superfield that describes the quantum states of a 12-dimensional supersymmetric particle. The particle has super phase space ${(X}^M{,P}^M,\Theta ),$ with a $\mathrm{}(10,2)\mathrm{}$ signature and 32 fermions. The worldline action is constructed as a generalization of the supersymmetric particle action in two-time physics. $\mathrm{SU}(2,2\mathrm{}|4)$ is a linearly realized global supersymmetry of the 2T action. The action is invariant under the gauge symmetries Sp $\mathrm{}(2,R),$ $\mathrm{SO}\mathrm{}(4,2),$ $\mathrm{SO}\mathrm{}\left(6\right),$ and fermionic kappa. These gauge symmetries ensure unitarity and causality while allowing the reduction of the 12-dimensional super phase space to the correct super phase space for ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ or $M^4\times R^6$ with 16 fermions and one time, or other dually related one time spaces. One of the predictions of this formulation is that all of the SU$(2,2\mathrm{}|4)$ representations that describe Kaluza-Klein towers in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ or $M^4\times R^6$ supergravity universally have vanishing eigenvalues for all the Casimir operators. This prediction has been partially verified directly in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ supergravity. This suggests that the supergravity spectrum supports a hidden $\mathrm{}(10,2)\mathrm{}$ structure. A possible duality between ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ and $M^4\times R^6$ supergravities is also indicated. Generalizations of the approach applicable 10-dimensional super Yang-Mills theory and 11-dimensional M theory are briefly discussed.

It is shown that all the states in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ supergravity have zero eigenvalue for all Casimir eigenvalues of its symmetry group SU(2,2|4). To compute this zero in supergravity we refine the oscillator methods for studying the lowest weight unitary representations of $\mathrm{SU}(N,M|R+S).\mathrm{}$ We solve the reduction problem when one multiplies an arbitrary number of super-doubletons. This enters in the computation of the Casimir eigenvalues of the lowest weight representations. We apply the results to SU(2,2|4) that classifies the Kaluza-Klein towers of ten-dimensional type IIB supergravity compactified on ${\mathrm{AdS}}_5\times {\mathrm{S}}^5.$ We show that the vanishing of the SU(2,2|4) Casimir eigenvalues for all the states is indeed a group-theoretical fact in ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ supergravity. By the AdS-CFT correspondence, it is also a fact for gauge invariant states of super-Yang-Mills theory with four supersymmetries in four dimensions. This nontrivial and mysterious zero is very interesting because it is predicted as a straightforward consequence of the fundamental local Sp(2) symmetry in 2T-physics. Via the 2T-physics explanation of this zero we find a global indication that these special supergravity and super-Yang-Mills theories hide a twelve-dimensional structure with (10,2) signature.

We extend our previous study on spherically symmetric braneworld solutions with induced gravity, including nonlocal bulk effects. We find the most general static four-dimensional black hole solutions with $g_{\mathrm{tt}}=-g_{\mathrm{rr}}^{-1}.$ They satisfy a closed system of equations on the brane and represent the strong-gravity corrections to the Schwarzschild-$\left(\mathrm{A}\right){\mathrm{dS}}_4$ spacetime. These new solutions have extra terms which give extra attraction relative to the Newtonian-$\left(\mathrm{A}\right){\mathrm{dS}}_4$ force; however, the conventional limits are easily obtained. These terms, when defined asymptotically, behave like ${\mathrm{AdS}}_4$ in this regime, while when defined at infinitely short distances they predict either an additional attractive Newtonian potential or an attractive potential which scales approximately as $\sqrt{r}.$ One of the solutions found gives extra deflection of light compared to Newtonian deflection.

In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.

We consider branes embedded in spacetimes of codimension 1 and 2, with a warped metric tensor for the subspace parallel to the brane. We study a variety of brane-world solutions arising by introducing a Schwarzschild-like black hole metric on the brane and we investigate the properties of the corresponding higher-dimensional spacetime. We demonstrate that normalizable bulk modes lead to a vanishing flow of energy through the naked singularities. From this point of view, these singularities are harmless.

We explore the cosmological solutions of classes of nonlinear bigravity theories. These theories are defined by effective four-dimensional Lagrangians describing the coupled dynamics of two metric tensors, and containing, in the linearized limit, both a massless graviton and an ultralight one. We focus on two paradigmatic cases: the case where the coupling between the two metrics is given by a Pauli-Fierz-type mass potential, and the case where this coupling derives from five-dimensional brane constructions. We find that cosmological evolutions in bigravity theories can be described in terms of the dynamics of two “relativistic particles,” moving in a curved Lorenzian space, and connected by some type of nonlinear “spring.” Classes of bigravity cosmological evolutions exhibit a “locking” mechanism under which the two metrics ultimately stabilize in a bi–de Sitter configuration, with relative (constant) expansion rates. In the absence of matter, we find that a generic feature of bigravity cosmologies is to exhibit a period of cosmic acceleration. This leads us to propose bigravity as a source of a new type of dark energy (“tensor quintessence”), exhibiting specific anisotropic features. Bigravity could also have been the source of primordial inflation.

We discuss the fully nonlinear formulation of multigravity. The concept of universality classes of effective Lagrangians describing bigravity, which is the simplest form of multigravity, is introduced. We show that nonlinear multigravity theories can naturally arise in several different physical contexts: brane configurations, certain Kaluza-Klein reductions and some non-commutative geometry models. The formal and phenomenological aspects of multigravity (including the problems linked to the linearized theory of massive gravitons) are briefly discussed.

Directional dark matter detectors will be able to record the recoil momentum spectrum of nuclei hit by dark matter WIMPs. We show that the recoil momentum spectrum is the Radon transform of the WIMP velocity distribution. This allows us to obtain analytic expressions for the recoil spectra of a variety of velocity distributions. We comment on the possibility of inverting the recoil momentum spectrum and obtaining the three-dimensional WIMP velocity distribution from data.