A brane-antibrane model for the entropy of neutral black branes is developed, following on from the work of Danielsson, Guijosa, and Kruczenski [J. High Energy Phys. 09, 011 (2001); Rev. Mex. Fis. 49S2, 61 (2003)]. The model involves equal numbers of $\mathrm{D}p$-branes and anti-$\mathrm{D}p$-branes, and arbitrary angular momenta, and covers the cases $p=0,1,2,3,4.\mathrm{}$ The thermodynamic entropy is reproduced by the strongly coupled field theory, up to a power of 2. The strong-coupling physics of the $p=0\mathrm{}$ case is further developed numerically, using techniques of Kabat and co-workers [Nucl. Phys. B571, 419 (2000); Phys. Rev. Lett. 86, 1426 (2001)], in the context of a toy model containing the tachyon and the bosonic degrees of freedom of the D0-brane and anti-D0-brane quantum mechanics. Preliminary numerical results show that strong-coupling finite-temperature stabilization of the tachyon is possible, in this context.

We discuss a previous attempt at a microscopic counting of the entropy of asymptotically flat nonextremal black holes. This method used string dualities to relate four and five dimensional black holes to the BTZ black hole. We show how the dualities can be justified in a certain limit, equivalent to a near horizon limit, but the resulting spacetime is no longer asymptotically flat.

A master action for bosonic strings and membranes, interpolating between the Nambu-Goto and Polyakov formalisms, is discussed. The role of the gauge symmetries in relation to reparametrization symmetries of the various actions is analyzed by a constrained Hamiltonian approach. This analysis reveals the difference between strings and higher branes, which is essentially tied to a familiar degree of freedom count. The cosmological term for membranes follows naturally in this scheme. The connection of our approach with the Arnowitt-Deser-Misner representation in general relativity is illuminated.

The Chern-Simons-like gravitational action is evaluated explicitly in four-dimensional space-time by radiative corrections at the one-loop level. The calculation is performed in the fermionic sector where the Dirac fermions interact with the background gravitational field, including the parity-violating term $\overline{\psi }b/{\gamma }_5\psi .$ The investigation takes into account the weak field approximation and dimensional regularization scheme.

We show that the Lorentz covariant formulation of $N=2\mathrm{}$ string in a curved space reveals an explicit hyper-Kähler structure. Apart from the metric, the superconformal currents couple to a background two-form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra.

The “geometric” and the “dynamic” variational principles are extended to the case of a classical test particle coupled with an external field through a scalar, velocity-independent term $\mathcal{U}.$ The relative Lagrangians are determined, and a super-Hamiltonian derivation of Hamilton-Jacobi equation for this case is also given. Consistency of results is shown throughout. Results thus found are then specialized to the case of the curved-spacetime motion of a classical polarized test particle, subject to the influence of an external electromagnetic field. We also consider the behavior of a spinning classical polarized test particle in a curved spacetime: the equations of motion are given, together with the equations describing the evolution of the spin.

We perform a complete integration of the Einstein-dilaton-antisymmetric form action describing black p-branes in arbitrary dimensions assuming the transverse space to be homogeneous and possessing spherical, toroidal, or hyperbolic topology. The generic solution contains eight parameters satisfying one constraint. Asymptotically flat solutions form a five-parametric subspace, while conditions of regularity of the nondegenerate event horizon further restrict this number to 3, which can be related to the mass and charge densities and the asymptotic value of the dilaton. In the case of a degenerate horizon, this number is reduced by 1. Our derivation constitutes a constructive proof of the uniqueness theorem for p-branes with the homogeneous transverse space. No asymptotically flat solutions with toroidal or hyperbolic transverse space within the considered class are shown to exist, which result can be viewed as a demonstration of the topological censorship for p-branes. From our considerations it follows, in particular, that some previously discussed p-brane-like solutions with extra parameters do not satisfy the standard conditions of asymptotic flatness and absence of naked singularities. We also explore the same system in presence of a cosmological constant and derive a complete analytic solution for higher-dimensional charged topological black holes, thus proving their uniqueness.

We consider solutions with conformal symmetry of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario. By assuming that the vector field generating the symmetry is nonstatic, the general solution of the field equations on the brane can be obtained in an exact parametric form, with the conformal factor taken as parameter. As a physical application of the obtained solutions we consider the behavior of the angular velocity of a test particle moving in a stable circular orbit. In this case the tangential velocity can be expressed as a function of the conformal factor and some integration constants only. For a specific range of integration constants, the tangential velocity of the test particle tends, in the limit of large radial distances, to a constant value. This behavior is specific to galactic rotation curves and is explained usually by invoking the hypothesis of dark matter. The limiting value of the angular velocity of the test particle can be obtained as a function of the baryonic mass and radius of the galaxy. The behavior of the dark radiation and dark pressure terms is also considered in detail, and it is shown that they can be expressed in terms of the rotational velocity of a test particle. Hence all the predictions of the present model can be tested observationally. Therefore the existence of the nonlocal effects, generated by the free gravitational field of the bulk in a conformally symmetric brane, may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic center.

We consider the effect of the ultraviolet (UV) or short wavelength modes on the background of brane gas cosmology. We find that the string matter sources are negligible in the UV and that the evolution is given primarily by the dilaton perturbation. We also find that the linear perturbations are well behaved and the predictions of brane gas cosmology are robust against the introduction of linear perturbations. In particular, we find that the stabilization of the extra dimensions (moduli) remains valid in the presence of dilaton and string perturbations.

We extend the theory of weak gravitational lensing to cosmologies with generalized gravity, described in the Lagrangian by a generic function depending on the Ricci scalar and a nonminimal coupled scalar field. We work out the generalized Poisson equations relating the dynamics of the fluctuating components to the two gauge-invariant scalar gravitational potentials, fixing the contributions from the modified background expansion and fluctuations. We show how the lensing equation gets modified by the cosmic expansion as well as by the presence of anisotropic stress, which is non-null at the linear level both in scalar-tensor gravity and in theories where the gravitational Lagrangian term features a nonminimal dependence on the Ricci scalar. Starting from the geodesic deviation, we derive the generalized expressions for the shear tensor and projected lensing potential, encoding the spacetime variation of the effective gravitational constant and isolating the contribution of the anisotropic stress, which introduces a correction due to the spatial correlation between the gravitational potentials. Finally, we work out the expressions of the lensing convergence power spectrum as well as the correlation between the lensing potential and the integrated Sachs-Wolfe effect affecting cosmic microwave background total intensity and polarization anisotropies. To illustrate phenomenologically the effects, we work out approximate expressions for the quantities above in extended quintessence scenarios where the scalar field coupled to gravity plays the role of the dark energy.

We recall and precise how light spin-0 particles could be acceptable dark matter candidates, and extend this analysis to spin-$\frac{1}{2}$ particles. We evaluate the (rather large) annihilation cross sections required, and show how they may be induced by a new light neutral spin-1 boson U. If this one is vectorially coupled to matter particles, the (spin-$\frac{1}{2}$ or spin-0) dark matter annihilation cross section into $e^{+}{e}^{-}$ automatically includes a $v_{\mathrm{dm}}^2$ suppression factor at threshold, as desirable to avoid an excessive production of $\gamma$ rays from residual dark matter annihilations. We also relate dark matter annihilations with production cross sections in $e^{+}{e}^{-}$ scatterings. Annihilation cross sections of spin-$\frac{1}{2}$ and spin-0 dark matter particles are given by exactly the same expressions. Just as for spin-0, light spin-$\frac{1}{2}$ dark matter particles annihilating into $e^{+}{e}^{-}$ could be responsible for the bright 511 keV $\gamma$ ray line observed by INTEGRAL from the galactic bulge.

It is shown that in a smooth hybrid inflation model in supergravity adiabatic fluctuations with a running spectral index with $n_s>1\mathrm{}$ on a large scale and $n_s<1\mathrm{}$ on a smaller scale can be naturally generated, as favored by the first-year data of WMAP. It is due to the balance between the nonrenormalizable term in the superpotential and the supergravity effect. However, since smooth hybrid inflation does not last long enough to reproduce the central value of observation, we invoke new inflation after the first inflation. Its initial condition is set dynamically during smooth hybrid inflation and the spectrum of fluctuations generated in this regime can have an appropriate shape to realize early star formation as found by WMAP. Hence two new features of WMAP observations are theoretically explained in a unified manner.

We point out that if heavy metastable particles composing the dark matter of our galaxy are responsible for the ultrahigh energy cosmic rays (UHECR) then the leading tidal stream of the Sagittarius dwarf galaxy could be detected through UHECR. The signal would be an anisotropy in the UHECR flux smaller than the telltale anisotropy towards the galactic center that would first establish unstable dark matter as the origin of the UHECR.

Clusters of galaxies are powerful cosmological probes, particularly if their masses can be determined. One possibility for mass determination is to study the cosmic microwave background (CMB) on small angular scales and observe deviations from a pure gradient due to lensing of massive clusters. I show that, neglecting contamination, this technique has the power to determine cluster masses very accurately, in agreement with estimates by Seljak and Zaldarriaga. However, the intrinsic small scale structure of the CMB significantly degrades this power. The resulting mass constraints are useless unless one imposes a prior on the concentration parameter c. With a modest prior on c, an ambitious CMB experiment ${(0.5\mathrm{}}^{\prime }$ resolution and $1\mu \mathrm{K}$ per pixel) could determine masses of high redshift $\mathrm{}(z>\mathrm{}0.7\mathrm{}),$ large $(M>\mathrm{}5\mathrm{}\times {10}^{14}{h}^{-1}{M}_{\odot })$ clusters with $\sim 30\%$ accuracy.

Weak gravitational lensing of background galaxies by foreground clusters offers an excellent opportunity to measure cluster masses directly without using gas as a probe. One source of noise which seems difficult to avoid is large scale structure along the line of sight. Here I show that the spatial properties of this noise are sufficiently distinct that it can be efficiently weeded out using standard map-making techniques.

We generate a complete basis of magnetic moment operators for the $N_c=3\mathrm{}$ ground-state baryons in the ${1/N}_c$ expansion, and compute and tabulate all associated matrix elements. We then compare to previous results derived in the literature and predict additional relations among baryon magnetic moments holding to subleading order in ${1/N}_c$ and flavor SU(3) breaking. Finally, we predict all unknown diagonal and transition magnetic moments to $<~0.15{\mu }_N$ accuracy, and suggest possible experimental measurements to improve the analysis even further.

The $b\overline{b}$ spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange potential between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings ${\Delta }_1={\rm Y}\left(1\mathrm{D}\right)-{\chi }_b\left(1\mathrm{P}\right)$ and other splittings between low-lying states are very sensitive to the QCD constant ${\Lambda }_{\mathrm{V}}{(n}_{\mathrm{f}})$ which occurs in the vector scheme, and good agreement with the experimental data is obtained for ${\Lambda }_{\mathrm{V}}(2\mathrm{}-\mathrm{loop},\hspace{0.5em}{n}_{\mathrm{f}}=5)=325\mathrm{}\pm 10\mathrm{MeV}$ which corresponds to the conventional ${\Lambda }_{\overline{\mathrm{MS}}}(2\mathrm{}-\mathrm{loop},n_{\mathrm{f}}=5)=238\mathrm{}\pm 7\mathrm{MeV},$ ${\alpha }_s(2\mathrm{}-\mathrm{loop},\hspace{0.5em}{M}_Z)=0.1189\mathrm{}\pm 0.0005,$ and to a large freezing value of the background coupling: ${\alpha }_{\mathrm{crit}}(2\mathrm{}-\mathrm{loop},\hspace{0.5em}{q}^2=0)={\alpha }_{\mathrm{crit}}(2\mathrm{}-\mathrm{loop},\hspace{0.5em}\overrightarrow{r}\infty )=0.58\mathrm{}\pm \mathrm{0.02.}$ If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling ${\alpha }_{\mathrm{static}}=\mathrm{const}$ is introduced, as in the Cornell potential, then precise agreement with ${\Delta }_1\left(\exp \right)$ and ${\Delta }_2\left(\exp \right)$ can be reached for the rather large Coulomb constant ${\alpha }_{\mathrm{static}}=0.43\mathrm{}\pm \mathrm{0.02.}$ We predict a value for the mass $M\left(2\mathrm{D}\right)=10451\mathrm{}\pm 2\mathrm{MeV}.$

We consider fermions on an extra dimensional interval. We find the boundary conditions at the ends of the interval that are consistent with the variational principle, and explain which ones arise in various physical circumstances. We apply these results to Higgsless models of electroweak symmetry breaking, where electroweak symmetry is not broken by a scalar vacuum expectation value, but rather by the boundary conditions of the gauge fields. We show that it is possible to find a set of boundary conditions for bulk fermions that would give a realistic fermion mass spectrum without the presence of a Higgs scalar, and present some sample fermion mass spectra for the standard model quarks and leptons as well as their resonances.

The presence of approximate electron number conservation and $\mu -\tau$ permutation symmetry of $S_2$ is shown to naturally provide bilarge neutrino mixing. First, the bimaximal neutrino mixing together with $U_{e3\mathrm{}}=0\mathrm{}$ is guaranteed to appear owing to $S_2,$ and then, the bilarge neutrino mixing together with $|U_{e3\mathrm{}}|\ll 1$ arises as a result of a tiny violation of $S_2.$ The observed mass hierarchy of $\Delta m_{\odot }^2$ $\ll$ $\Delta m_{\mathrm{atm}}^2$ is subject to another tiny violation of the electron number conservation. This scenario is realized in a specific model based on ${\mathrm{SU}\left(3\right)\mathrm{}}_L\times {U\left(1\right)\mathrm{}}_N$ with two-loop radiative mechanism for neutrino masses. The radiative effects from heavy leptons contained in lepton triplets generate the bimaximal structure, and those from charged leptons, which break $S_2,$ generate the bilarge structure together with $|U_{e3\mathrm{}}|\ll 1.$ To suppress dangerous flavor-changing neutral current interactions due to Higgs exchanges especially for quarks, this $S_2$ symmetry is extended to a discrete $Z_8$ symmetry, which also ensures the absence of a one-loop radiative mechanism.

We study the dynamical symmetry breaking in the gauge-Higgs unification of the five-dimensional theory compactified on an orbifold, $S^1{/Z}_2.$ This theory identifies Wilson line degrees of freedom as “Higgs doublets.” We consider ${\mathrm{SU}\left(3\right)\mathrm{}}_c\times {\mathrm{SU}\left(3\right)\mathrm{}}_W$ and $\mathrm{SU}\left(6\right)\mathrm{}$ models with the compactification scale of order of a few TeV. The gauge symmetries are reduced to ${\mathrm{SU}\left(3\right)\mathrm{}}_c\times {\mathrm{SU}\left(2\right)\mathrm{}}_L\times {U\left(1\right)\mathrm{}}_Y$ and ${\mathrm{SU}\left(3\right)\mathrm{}}_c\times {\mathrm{SU}\left(2\right)\mathrm{}}_L\times {U\left(1\right)\mathrm{}}_Y\times U\left(1\right),$ respectively, through the orbifolding boundary conditions. We estimate the one loop effective potential of “Higgs doublets,” and find that the electroweak breaking is realized through the radiative corrections when there are suitable numbers of bulk fields possessing the suitable representations. The masses of “Higgs doublets” are O(100) GeV in this scenario.