We consider tachyonic string-field fluctuations about a $\mathrm{D}p$-brane background in the geometrical (CFT) formulation of vacuum string field theory. We then extend this analysis to the case of a background B field. We find that the standard results for D-brane tension are reproduced in both cases.

We continue our investigation of the phenomenological implications of the “deformed” commutation relations $[x_i,p_j]=iħ\left[\right(1+\beta p^2){\delta }_{\mathrm{ij}}+{\beta }^{\prime }{p}_i{p}_j].$ These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.

We consider the classification of BPS and non-BPS D-branes in orientifold models. In particular we construct all stable BPS and non-BPS D-branes in the Gimon-Polchinski (GP) and Dabholkar-Park-Blum-Zaffaroni (DPBZ) orientifolds and determine their stability regions in moduli space as well as decay products. We find several kinds of integrally and torsion charged non-BPS D-branes. Certain of these are found to have projective representations of the $\mathrm{orientifold}\times \mathrm{GSO}$ group on the Chan-Paton factors. It is found that the GP orientifold is not described by equivariant orthogonal K-theory as may have been at first expected. Instead a twisted version of this K-theory is expected to be relevant.

We compute the finite temperature induced fermion number for fermions coupled to a static nonlinear sigma model background in $2+1$ dimensions, in the derivative expansion limit. While the zero temperature induced fermion number is well known to be topological (it is the winding number of the background), at finite temperature there is a temperature dependent correction that is nontopological—this finite T correction is sensitive to the detailed shape of the background. At low temperature we resum the derivative expansion to all orders, and we consider explicit forms of the background as a $\mathcal{C}{\mathcal{P}}^1$ instanton or as a baby Skyrmion.

Stability and instability bands in classical mechanics are well studied in connection with systems such as described by the Mathieu equation. We examine whether such band structure can arise in classical field theory in the context of an embedded kink in 1+1 dimensions. The static embedded kink is unstable to perturbations but we show that if the kink is dynamic it can exhibit stability in certain parameter bands. Our results are relevant for estimating the lifetimes of various embedded defects and, in particular, loops of electroweak Z string.

We probe the $U\left(N\right)\mathrm{}$ chiral Gross-Neveu model with a source term $J\overline{\Psi }\Psi .$ We find an expression for the renormalization scheme and scale invariant source $Ĵ,$ as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter d. We obtain a nonperturbative mass gap as the solution of $Ĵ=0.\mathrm{}$ A physical choice for d gives good results for $N>\mathrm{}2.\mathrm{}$ The self-consistent minimal sensitivity condition gives a slight improvement.

We compare recent numerical results, obtained within a “helical Killing vector” approach, on circular orbits of corotating binary black holes to the analytical predictions made by the effective one-body (EOB) method (which has been recently extended to the case of spinning bodies). On the scale of the differences between the results obtained by different numerical methods, we find good agreement between numerical data and analytical predictions for several invariant functions describing the dynamical properties of circular orbits. This agreement is robust against the post-Newtonian accuracy used for the analytical estimates, as well as under choices of the resummation method for the EOB “effective potential,” and gets better as one uses a higher post-Newtonian accuracy. These findings open the way to a significant “merging” of analytical and numerical methods, i.e. to matching an EOB-based analytical description of the (early and late) inspiral, up to the beginning of the plunge, to a numerical description of the plunge and merger. We illustrate also the “flexibility” of the EOB approach, i.e. the possibility of determining some “best fit” values for the analytical parameters by comparison with numerical data.

The differential cross section for scattering of a Dirac particle in a black hole background is found. The result is the gravitational analogue of the Mott formula for scattering in a Coulomb background. The equivalence principle is neatly embodied in the cross section, which depends only on the incident velocity, and not the particle mass. The low angle limit agrees with classical calculations based on the geodesic equation. The calculation employs a well-defined iterative scheme which can be extended to higher orders. Repeating the calculation in different gauges shows that our result for the cross section is gauge invariant and highlights the issues involved in setting up a sensible iterative scheme.

What is the nature of the energy spectrum of a black hole? The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As stressed long ago by Mukhanov, such eigenvalues must be exponentially degenerate with respect to the area quantum number if one is to understand black hole entropy as reflecting degeneracy of the observable states. Here we construct the black hole stationary states by means of a pair of “creation operators” subject to a particular simple algebra, a slight generalization of that for a pair of harmonic oscillators. This algebra reproduces the main features of the algebraic approach, in particular the equally spaced area spectrum. We then prove rigorously that the $n\mathrm{th}$ area eigenvalue is exactly $2^n$-fold degenerate. Thus black hole entropy qua logarithm of the number of states for a fixed horizon area is indeed proportional to that area.

We discuss quantum mechanics in the moduli space consisting of two maximally charged dilaton black holes. The quantum mechanics of the two-black-hole system is similar to the one of the de Alfaro–Fubini–Furlan model, and this system has the $\mathrm{SL}(2,R)\mathrm{}$ conformal symmetry. Also, we discuss the bound states in this system.

In this paper we propose that the accelerating expansion of the present matter-dominated universe, as suggested by the recent distance measurements of type Ia supernovae, is generated along with the evolution of space in extra dimensions. The Einstein equations are first analyzed qualitatively and then solved numerically, so as to exhibit explicitly these patterns of the accelerating expansion in this scenario. A fine-tuning problem associated with such a scenario is also described and discussed.

The Cardy-Verlinde formula is further verified by using the Kerr-Newman-${\mathrm{AdS}}_4$ and ${\mathrm{K}\mathrm{e}\mathrm{r}\mathrm{r}-\mathrm{N}\mathrm{e}\mathrm{w}\mathrm{m}\mathrm{a}\mathrm{n}-\mathrm{d}\mathrm{S}}_4$ black holes. In the Kerr-Newman-${\mathrm{AdS}}_4$ spacetime, we find that, for strongly coupled CFTs with AdS duals, to cast the entropy of CFT into the Cardy-Verlinde formula the Casimir energy must contain the terms $-n(\mathcal{J}{\Omega }_H+Q\Phi /2+Q{\Phi }_0/2),$ which are associated with rotational and electric potential energies, and the extensive energy includes the term $-Q{\Phi }_0.$ For the Kerr-Newman-${\mathrm{dS}}_4$ black hole, we note that the Casimir energy is negative but the extensive energy is positive on the cosmological horizon, while the Casimir energy is positive but the extensive energy is negative on the event horizon (the definitions for the two energies possess the same forms as the corresponding quantities of the Kerr-Newman-${\mathrm{AdS}}_4$ black hole). Thus we have to take the absolute value of the Casimir (extensive) energy in the Cardy-Verlinde formula for the cosmological (event) horizon. The result for the Kerr-Newman-${\mathrm{dS}}_4$ spacetime provides support of the dS-CFT correspondence. Furthermore, we also obtain the Bekenstein-Verlinde-like entropy bound for the Kerr-Newman-${\mathrm{AdS}}_4$ black hole and the D bound on the entropy of the matter system in Kerr-Newman-${\mathrm{dS}}_4$ spacetime. We find that both bounds are tightened by the electric charge.

We extend our recent work on the effects of a time-varying fine-structure constant $\alpha$ in the cosmic microwave background by providing a thorough analysis of the degeneracies between $\alpha$ and the other cosmological parameters, and discussing ways to break these with both existing and/or forthcoming data. In particular, we present the state-of-the-art cosmic microwave background constraints on $\alpha$ through a combined analysis of the BOOMERanG, MAXIMA and DASI data sets. We also present a novel discussion of the constraints on $\alpha$ coming from large-scale structure observations, focusing in particular on the power spectrum from the 2dF survey. Our results are consistent with no variation in $\alpha$ from the epoch of recombination to the present day, and restrict any such variation to be less than about $4\%.$ We show that the forthcoming Microwave Anisotropy Probe and Planck experiments will be able to break most of the currently existing degeneracies between $\alpha$ and other parameters, and measure $\alpha$ to better than percent accuracy.

We analyze the effect of the Sun’s gravitational field on a flow of cold dark matter (CDM) through the solar system in the limit where the velocity dispersion of the flow vanishes. The exact density and velocity distributions are derived in the case where the Sun is a point mass. The results are extended to the more realistic case where the Sun has a finite size spherically symmetric mass distribution. We find that regions of infinite density, called caustics, appear. One such region is a line caustic on the axis of symmetry, downstream from the Sun, where the flow trajectories cross. Another is a cone-shaped caustic surface near the trajectories of maximum scattering angle. The trajectories forming the conical caustic pass through the Sun’s interior and probe the solar mass distribution, raising the possibility that the solar mass distribution may some day be measured by a dark matter detector on Earth. We generalize our results to the case of flows with continuous velocity distributions, such as that predicted by the isothermal model of the Milky Way halo.

Galactic dark matter can be modeled by a scalar field coupled to standard gravity in order to effectively modify Kepler’s law. In particular, we show that a solvable toy model with a self-interaction $U\left(\Phi \right)$ borrowed from nontopological solitons produces already qualitatively correct rotation curves. Although the relativistic effects in the halo are very small, our generally relativistic formulation aids at reconstructing more realistic scalar models with self-interaction.

It is an accepted practice in cosmology to invoke a scalar field with a potential $V\left(\phi \right)$ when the observed evolution of the universe cannot be reconciled with theoretical prejudices. Since one function degree of freedom in the expansion factor $a\left(t\right)\mathrm{}$ can be traded off for the function $V\left(\phi \right),$ it is always possible to find a scalar field potential which will reproduce a given evolution. I provide a recipe for determining $V\left(\phi \right)$ from $a\left(t\right)\mathrm{}$ in two cases: (i) a normal scalar field with the Lagrangian $\mathcal{L}=(1/2)\mathrm{}{\partial }_a\phi {\partial }^a\phi -V\left(\phi \right)$ used in quintessence or dark energy models; (ii) a tachyonic field with the Lagrangian $\mathcal{L}=-V\left(\phi \right)[1-{\partial }_a\phi \partial {}^a\phi {]}^{1/2},$ motivated by recent string theoretic results. In the latter case, it is possible to have accelerated expansion of the universe during the late phase in certain cases.

We propose to modify the saturation model of Golec-Biernat and Wüsthoff by including Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution. We find considerable improvement for the total deep inelastic cross section, in particular in the large $Q^2$ region. The successful description of deep inelastic scattering diffraction is preserved.

A combined statistical analysis of the experimental results of the LSND and KARMEN ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ oscillation search is presented. LSND has evidence for neutrino oscillations that is not confirmed by the KARMEN experiment. This joint analysis is based on the final likelihood results for both data sets. A frequentist approach is applied to deduce confidence regions. At a combined confidence level of 36%, there is no area of oscillation parameters compatible with both experiments. For the complementary confidence of $1-0.36=64\%,$ there are two well defined regions of oscillation parameters $\left({\sin }^2\right(2\mathrm{}\Theta ),\Delta m^2)$ compatible with both experiments.

Recent data from lattice measurements of gauge-invariant nonlocal scalar quark condensates are analyzed to extract the short-distance correlation length $1/{\lambda }_q$ and to construct an admissible Ansatz for the condensate behavior in a coordinate space. The correlation length values for both the quenched and full-QCD cases appear in good agreement with the well-known QCD sum-rule (SR) estimates of the mixed quark-gluon condensate $2{\lambda }_q^2=〈\overline{q}\left(ig{\sigma }_{\mu \nu }{G}_{\mu \nu }\right)q〉/〈\overline{q}q〉=0.8\mathrm{}–1.1{\mathrm{GeV}}^2.$ We test two different Ansätze for a nonlocal quark condensate and trace their influence on the twist-2 pion distribution amplitude by means of QCD SR’s. The main features of the pion distribution amplitude are confirmed by the CLEO experimental results.

The relative smoothing rates of various gauge field smoothing algorithms are investigated on $\mathcal{O}{(a}^2)$-improved SU(3) Yang-Mills gauge field configurations. In particular, an $\mathcal{O}{(a}^2)$-improved version of APE smearing is motivated by considerations of smeared link projection and cooling. The extent to which the established benefits of improved cooling carry over to improved smearing is critically examined. We consider representative gauge field configurations generated with an $\mathcal{O}{(a}^2)$-improved gauge field action on ${16}^3\times 32$ lattices at $\beta =4.38\mathrm{}$ and ${24}^3\times 36$ lattices at $\beta =5.00\mathrm{}$ having lattice spacings of 0.165(2) fm and 0.077(1) fm, respectively. While the merits of improved algorithms are clearly displayed for the coarse lattice spacing, the fine lattice results put the various algorithms on a more equal footing and allow a quantitative calibration of the smoothing rates for the various algorithms. We find the relative rate of variation in the action may be succinctly described in terms of simple calibration formulas which accurately describe the relative smoothness of the gauge field configurations at a microscopic level.