We exploit the Seiberg-Witten maps for fields and currents in a $\mathrm{U}(1)$ gauge theory relating the noncommutative and commutative (usual) descriptions to obtain the $\mathrm{O}(\theta )$ structure of the commutator anomalies in noncommutative electrodynamics. These commutators involve the (covariant) current-current algebra and the (covariant) current-field algebra. We also establish the compatibility of the anomalous commutators with the noncommutative covariant anomaly through the use of certain consistency conditions derived here.

We have constructed the appropriate Hamiltonian of the noncommutative Coulombic monopole (i.e. the noncommutative hydrogen atom with a monopole). The energy levels of this system have been calculated, discussed, and compared with the noncommutative hydrogen atom ones. The main emphasis is put on the ground state. In addition, the Stark effect for the noncommutative Coulombic monopole has been studied.

We search for acoustic analogues of a spherical symmetric black hole with a pointlike source. We show that the gravitational system has a dynamical counterpart in the constrained, steady motion of a fluid with a planar source. The equations governing the dynamics of the gravitational system can be exactly mapped in those governing the motion of the fluid. The different meaning that singularities and sources have in fluid dynamics and in general relativity is also discussed. Whereas in the latter a pointlike source is always associated with a (curvature) singularity in the former the presence of sources does not necessarily imply divergences of the fields.

In a recent paper [I. P. Neupane and D. L. Wiltshire, Phys. Lett. B 619, 201 (2005).] we have found a new class of accelerating cosmologies arising from a time-dependent compactification of classical supergravity on product spaces that include one or more geometric twists along with nontrivial curved internal spaces. With such effects, a scalar potential can have a local minimum with positive vacuum energy. The existence of such a minimum generically predicts a period of accelerated expansion in the four-dimensional Einstein conformal frame. Here we extend our knowledge of these cosmological solutions by presenting new examples and discuss the properties of the solutions in a more general setting. We also relate the known (asymptotic) solutions for multiscalar fields with exponential potentials to the accelerating solutions arising from simple (or twisted) product spaces for internal manifolds.

We investigate the way big rips are approached in a fully inhomogeneous description of the space-time geometry. If the pressure and energy densities are connected by a (supernegative) barotropic index, the spatial gradients and the anisotropic expansion decay as the big rip is approached. This behavior is contrasted with the usual big-bang singularities. A similar analysis is performed in the case of sudden (quiescent) singularities and it is argued that the spatial gradients may well be non-negligible in the vicinity of pressure singularities.

During the past year, a minimal renormalizable supersymmetric SO(10) model has been proposed with the following properties: it predicts a naturally stable dark matter and neutrino mixing angles ${\theta }_{\mathrm{atm}}$ and ${\theta }_{13}$ while at the same time accommodating Cabibbo-Kobayashi-Maskawa $CP$ violation among quarks with no supersymmetry (SUSY) $CP$ problem. Suppression of proton decay for all allowed values of $\tan \beta$ strongly restricts the flavor structure of the model making it predictive for other processes as well. We discuss the following predictions of the model in this paper, e.g. down-type quark masses, and neutrino oscillation parameters, $U_{e3}$, ${\delta }_{\mathrm{MNSP}}$, which will be tested by long baseline experiments such as T2K and subsequent experiments using the neutrino beam from JPARC. We also calculate lepton flavor violation and the lepton asymmetry of the Universe in this model.

The left-right supersymmetric model contains a right-handed gaugino, as well as several Higgsinos, in addition to the minimal supersymmetric model. Thus several $CP$-noninvariant phases appear in this sector. We analyze their impact on chargino masses and find that only two combinations are physically relevant. We then study the production of charginos in $e^{+}{e}^{-}$ annihilation and chargino decays into a sneutrino and a lepton, and investigate the effects of $CP$-phases. We also study the $CP$-odd asymmetry in the production and subsequent decay at the linear collider with longitudinally polarized beams and find a large enhancement when the decay channel to the right sneutrino is available. The effects of the phases in the left-right supersymmetric chargino sector are different from the minimal supersymmetric standard model, and signals from this sector would be able to distinguish between different gauge symmetries.

We gauge the impact of soft-gluon resummation on quark distributions by performing a simple fit of deep inelastic scattering structure function data using next-to-leading order (NLO) and next-to-leading-logarithmic- (NLL)-resummed coefficient functions. We make use of NuTeV charged-current data, as well as New Muon Collaboration (NMC) and Bologna-CERN-Dubna-Munich-Saclay (BCDMS) neutral-current results, which probe large values of $x$. Our results suggest that the inclusion of resummation effects in global fits of parton distributions is both feasible and desirable, in order to achieve at large $x$ the accuracy goals of the LHC physics program.

Single top-quark production, via weak-interaction processes, is an important test of the standard model, potentially sensitive to new physics. However, it is becoming known that this measurement is much more challenging at the Tevatron than originally expected. We reexamine this process and suggest new methods, using shape variables, that can supplement the methods that have been discussed previously. In particular, by focusing on correlations and asymmetries, we can reduce backgrounds substantially without low acceptance for the signal. Our method also allows for a self-consistency check on the modeling of the backgrounds. However, at the present time, serious systematic problems remain, especially concerning the background from $W$-plus-jets; these must be studied further by experimentalists and theorists alike.

Some years ago, Cho and Vilenkin, introduced a model which presents topological solutions, despite not having degenerate vacua as is usually expected. Here we present a new model with topological defects, connecting degenerate vacua but which in a certain limit recovers precisely the one proposed originally by Cho and Vilenkin. In other words, we found a kind of parent model for the so called vacuumless model. Then the idea is extended to a model recently introduced by Bazeia et al. Finally, we trace some comments the case of the Liouville model.

We study the effective $D=4$, $\mathcal{N}=1$ supergravity description of five-dimensional heterotic M theory in the presence of an M5 brane, and derive the Killing vectors and isometry group for the Kähler moduli-space metric. The group is found to be a non-semi-simple maximal parabolic subgroup of $Sp(4,\mathbb{R})$, containing a nontrivial $SL(2,\mathbb{R})$ factor. The underlying moduli space is then naturally realized as the group space $Sp(4,\mathbb{R})/U(2)$, but equipped with a nonhomogeneous metric that is invariant only under that maximal parabolic group. This nonhomogeneous metric space can also be derived via field truncations and identifications performed on $Sp(8,\mathbb{R})/U(4)$ with its standard homogeneous metric. In a companion paper we use these symmetries to derive new cosmological solutions from known ones.

The Casimir and van der Waals interaction between two dissimilar thick dielectric plates is reconsidered on the basis of thermal quantum field theory in Matsubara formulation. We briefly review two main derivations of the Lifshitz formula in the framework of thermal quantum field theory without use of the fluctuation-dissipation theorem. A set of special conditions is formulated under which these derivations remain valid in the presence of dissipation. The low-temperature behavior of the Casimir and van der Waals interactions between dissimilar dielectrics is found analytically from the Lifshitz theory for both an idealized model of dilute dielectrics and for real dielectrics with finite static dielectric permittivities. The free energy, pressure, and entropy of the Casimir and van der Waals interactions at low temperatures demonstrate the same universal dependence on the temperature as was previously discovered for ideal metals. The entropy vanishes when temperature goes to zero proving the validity of the Nernst heat theorem. This solves the long-standing problem on the consistency of the Lifshitz theory with thermodynamics in the case of dielectric plates. The obtained asymptotic expressions are compared with numerical computations for both dissimilar and similar real dielectrics and found to be in excellent agreement. The role of the zero-frequency term in Matsubara sum is investigated in the case of dielectric plates. It is shown that the inclusion of conductivity in the model of dielectric response leads to the violation of the Nernst heat theorem. The applications of this result to the topical problems of noncontact atomic friction and the Casimir interaction between real metals are discussed.

We study Lorentz-violating models of massive gravity which preserve rotations and are invariant under time-dependent shifts of the spatial coordinates. In the linear approximation the Newtonian potential in these models has an extra confining term proportional to the distance from the source. We argue that during cosmological expansion the Universe may be driven to an attractor point with larger symmetry which includes particular simultaneous dilatations of time and space coordinates. The confining term in the potential vanishes as one approaches the attractor. In the vicinity of the attractor the extra contribution is present in the Friedmann equation which, in a certain range of parameters, gives rise to the cosmic acceleration.

The Dvali-Gabadadze-Porrati (DGP) model with additional terms in the action is considered. These terms have a special form and include auxiliary scalar fields without kinetic terms, which are nonminimally coupled to gravity. The use of these fields allows one to exclude the mode, which corresponds to the strong coupling effect, from the theory. Effective four-dimensional theory on the brane appears to be the same, as in the original DGP model.

The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna. This paper calculates, using a semirelativistic approximation, the total energy and angular momentum lost to gravitational radiation by compact bodies on very high eccentricity orbits passing close to a supermassive, nonspinning black hole; these quantities determine the characteristics of the orbital evolution necessary to estimate the capture rate. The semirelativistic approximation improves upon treatments which use orbits at Newtonian order and quadrupolar radiation emission, and matches well onto accurate Teukolsky simulations for low eccentricity orbits. Formulas are presented for the semirelativistic energy and angular momentum fluxes as a function of general orbital parameters.

We present a simple way to calculate non-Gaussianity in inflation using fully nonlinear equations on long wavelengths with stochastic sources to take into account the short-wavelength quantum fluctuations. Our formalism includes both scalar metric and matter perturbations, combining them into variables which are invariant under changes of time slicing in the long-wavelength limit. We illustrate this method with a perturbative calculation in the single-field slow-roll case. We also introduce a convenient choice of variables to graphically present the full momentum dependence of the three-point correlator.

We fit the ultrahigh energy cosmic ray spectra above ${10}^{19}\mathrm{eV}$ with different injection spectra at cosmic ray sources that are uniformly and homogeneously distributed in the Universe. We conclude that the current ultrahigh energy spectra are consistent with power laws of index $\alpha$ between 2.4 and 2.7. There is a slow dependence of these indices on the cosmological evolution of the cosmic ray sources, which in this model determines the end of the galactic cosmic rays spectrum.

The idea of quark-lepton universality at high energies has been introduced as a natural extension to the standard model. This is achieved by endowing leptons with new degrees of freedom—leptonic color, an analogue of the familiar quark color. Grand and partially unified models which utilize this new gauge symmetry $SU(3{)}_{\ell }$ have been proposed in the context of the quartification gauge group $SU(3{)}^4$. Phenomenologically successful gauge coupling constant unification without supersymmetry has been demonstrated for cases where the symmetry breaking leaves a residual $SU(2{)}_{\ell }$ unbroken. Though attractive, these schemes either incorporate ad hoc discrete symmetries and nonrenormalizable mass terms, or achieve only partial unification. We show that grand unified models can be constructed where the quartification group can be broken fully [i.e. no residual $SU(2{)}_{\ell }$] to the standard model gauge group without requiring additional discrete symmetries or higher dimension operators. These models also automatically have suppressed nonzero neutrino masses. We perform a systematic analysis of the renormalization-group equations for all possible symmetry breaking routes from $SU(3{)}^4\to SU(3{)}_q\otimes SU(2{)}_L\otimes U(1{)}_Y$. This analysis indicates that gauge coupling unification can be achieved for several different symmetry breaking patterns and we outline the requirements that each gives on the unification scale. We also show that the unification scenarios of those models which leave a residual $SU(2{)}_{\ell }$ symmetry are not unique. In both symmetry breaking cases, some of the scenarios require new physics at the TeV scale, while others do not allow for new TeV phenomenology in the fermionic sector.

We study the nuclear ${\mu }^{-}-e^{-}$ conversion in the general framework of the effective Lagrangian approach without referring to any specific realization of the physics beyond the standard model (SM) responsible for lepton flavor violation (LFV). We analyze the role of scalar meson exchange between the lepton and nucleon currents and show its relevance for the coherent channel of ${\mu }^{-}-e^{-}$conversion. We show that this mechanism introduces modifications in the predicted ${\mu }^{-}-e^{-}$ conversion rates in comparison with the conventional direct nucleon mechanism, based on the contact type interactions of the nucleon currents with the LFV leptonic current. We derive from the experimental data lower limits on the mass scales of the generic LFV lepton-quark contact terms and demonstrate that they are more stringent than the similar limits existing in the literature.

We compute the one-loop effective action in $\mathcal{N}=1$ superconformal $SU(N)$ gauge theory which is an exactly marginal deformation of the $\mathcal{N}=4$ SYM. We consider an Abelian background of constant $\mathcal{N}=1$ gauge field and single chiral scalar. While for finite $N$ the effective action depends nontrivially on the deformation parameter $q=e^{i\pi \beta }$, this dependence disappears in the large $N$ limit if the parameter $\beta$ is real. This conclusion matches the strong-coupling prediction coming from the form of a D3-brane probe action in the dual supergravity background: for the simplest choice of the D3-brane position the probe action happens to be the same as for a D3-brane in $Ad{S}_5\times S^5$ placed parallel to the boundary of $Ad{S}_5$. This suggests that in the real $\beta$ deformation case there exists a large $N$ nonrenormalization theorem for the $F^4$ term in the action.