We study the Regge limit of string amplitudes within the model of Polchinski-Strassler for string scattering in warped spacetimes. We also present some numerical estimations of the Regge slopes and intercepts. It is quite remarkable that the real values of those are inside a range of ours.

First, I present two new classes of magnetic rotating solutions in four-dimensional Einstein-Maxwell-dilaton gravity with Liouville-type potential. The first class of solutions yields a four-dimensional spacetime with a longitudinal magnetic field generated by a static or spinning magnetic string. I find that these solutions have no curvature singularity and no horizons, but have a conic geometry. In these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. The second class of solutions yields a spacetime with an angular magnetic field. These solutions have no curvature singularity, no horizon, and no conical singularity. The net electric charge of the strings in these spacetimes is proportional to their velocities. Second, I obtain the ($n+1$)-dimensional rotating solutions in Einstein-dilaton gravity with Liouville-type potential. I argue that these solutions can present horizonless spacetimes with conic singularity, if one chooses the parameters of the solutions suitable. I also use the counterterm method and compute the conserved quantities of these spacetimes.

We use the numerical solution describing the evolution of a perturbed black string presented by M. Choptuik, L. Lehner, I. Olabarrieta, R. Petryk, F. Pretorius, and H. Villegas [Phys. Rev. D 68, 044001 (2003)] to elucidate the intrinsic behavior of the horizon. It is found that by the end of the simulation, the affine parameter on the horizon has become very large and the expansion and shear of the horizon in turn very small. This suggests the possibility that the horizon might pinch off in infinite affine parameter.

We study the implications of a noncommutative geometry of the minisuperspace variables for the Friedmann-Robertson-Walker universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution in four different scenarios: classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative, the last two employing the Bohmian formalism of quantum trajectories. The role of noncommutativity is discussed by drawing a parallel between its realizations in two possible frameworks for physical interpretation: the NC frame, where it is manifest in the universe degrees of freedom, and in the C frame, where it is manifest through $\theta$-dependent terms in the Hamiltonian. As a result of our comparative analysis, we find that noncommutative geometry can remove singularities in the classical context for sufficiently large values of $\theta$. Moreover, under special conditions, the classical noncommutative model can admit bouncing solutions characteristic of the commutative quantum Friedmann-Robertson-Walker universe. In the quantum context, we find nonsingular universe solutions containing bounces or being periodic in the quantum commutative model. When noncommutativity effects are turned on in the quantum scenario, they can introduce significant modifications that change the singular behavior of the universe solutions or that render them dynamical whenever they are static in the commutative case. The effects of noncommutativity are completely specified only when one of the frames for its realization is adopted as the physical one. Nonsingular solutions in the NC frame can be mapped into singular ones in the C frame.

The gravitational wave (GW) signals emitted by a network of cosmic strings are reexamined in view of the possible formation of a network of cosmic superstrings at the end of brane inflation. The reconnection probability $p$ of intersecting fundamental or Dirichlet strings might be much smaller than 1, and the properties of the resulting string network may differ significantly from those of ordinary strings (which have $p=1$). In addition, it has been recently suggested that the typical length of newly formed loops may differ by a factor $ϵ\ll 1$ from its standard estimate. Here, we analyze the effects of the two parameters $p$ and $ϵ$ on the GW signatures of strings. We consider both the GW bursts emitted from cusps of oscillating string loops, which have been suggested as candidate sources for the LIGO/VIRGO and LISA interferometers, and the stochastic GW background, which may be detectable by pulsar-timing observations. In both cases we find that previously obtained results are quite robust, at least when the loop sizes are not suppressed by many orders of magnitude relative to the standard scenario. We urge pulsar observers to reanalyze a recently obtained 17-yr combined data set to see whether the large scatter exhibited by a fraction of the data might be due to a transient GW burst activity of some sort, e.g., to a near cusp event.

We provide a simple but robust argument that primordial black hole production generically does not exceed astrophysical bounds during the resonant preheating phase after inflation. This conclusion is supported by fully nonlinear lattice simulations of various models in two and three dimensions which include rescattering but neglect metric perturbations. We examine the degree to which preheating amplifies density perturbations at the Hubble scale and show that, at the end of the parametric resonance, power spectra are universal, with no memory of the power spectrum at the end of inflation. In addition, we show how the probability distribution of density perturbations changes from exponential on very small scales to Gaussian when smoothed over the Hubble scale—the crucial length for studies of primordial black hole formation—hence justifying the standard assumption of Gaussianity.

We present a systematic analysis of all the contributions at the leading log order to the branching ratio of the inclusive radiative decay $B\to X_s+\gamma$ in the framework of supersymmetry without $R$ parity. The relevant set of four-quark operators involved in QCD running are extended from six (within the standard model and the minimal supersymmetric standard model) to 24, with also many new contributions to the Wilson coefficients of (chromo)magnetic penguins for either chiral structure. We present complete analytical results here without any a priori assumptions on the form of $R$-parity violation. Mass-eigenstate expressions are given; hence the results are free from the commonly adopted mass-insertion approximation. In the numerical analysis, we focus here only on the influence of the trilinear ${\lambda }_{ijk}^{\prime }$ couplings and report on the possibility of a few orders of magnitude improvement for the bounds on a few combinations of the ${\lambda }^{\prime }$ couplings. Our study shows that the Wilson coefficients of the current-current operators due to $R$-parity violation dominate over the direct contributions to the penguins. However, the interplay of various contributions is complicated due to the QCD corrections which we elaborate here.

In a model in which quarks and leptons are built up from two spin-$\frac{1}{2}$ preons as fundamental entities, a new class of fermionic bound states (hyperquarks) arises. It turns out that these hyperquarks are necessary to fulfill the ’t Hooft anomaly constraint, which then links the number of fermionic generations to the number of colors and hypercolors.

We perform a nonperturbative determination of the $O(a)$-improvement coefficient $c_{\mathrm{S}\mathrm{W}}$ for the Wilson quark action in three-flavor QCD with the plaquette gauge action. Numerical simulations are carried out in a range of $\beta =12.0–5.2$ on a single lattice size of $8^3\times 16$ employing the Schrödinger functional setup of lattice QCD. As our main result, we obtain an interpolation formula for $c_{\mathrm{S}\mathrm{W}}$ and the critical hopping parameter $K_c$ as a function of the bare coupling. This enables us to remove the $O(a)$ scaling violation from physical observables in future numerical simulation in the wide range of $\beta$. Our analysis with a perturbatively modified improvement condition for $c_{\mathrm{S}\mathrm{W}}$ suggests that finite volume effects in $c_{\mathrm{S}\mathrm{W}}$ are not large on the $8^3\times 16$ lattice. We investigate $N_f$ dependence of $c_{\mathrm{S}\mathrm{W}}$ by additional simulations for $N_f=4$, 2, and 0 at $\beta =9.6$. As a preparatory step for this study, we also determine $c_{\mathrm{S}\mathrm{W}}$ in two-flavor QCD at $\beta =5.2$. At this $\beta$, several groups have carried out large-scale calculations of the hadron spectrum, while no systematic determination of $c_{\mathrm{S}\mathrm{W}}$ has been performed.

The electromagnetic properties of baryons containing a heavy quark are calculated at next-to-leading order in partially quenched heavy hadron chiral perturbation theory. Calculations are performed for three light flavors in the isospin limit and additionally for two light nondegenerate flavors. We use partially quenched charge matrices that are easy to implement on the lattice. The results presented are necessary for the light-quark mass extrapolation and zero-momentum extrapolation of lattice QCD and partially quenched lattice QCD calculations of heavy hadron electromagnetic properties. Additionally relations between the sextet electromagnetic form factors and transition form factors are derived.

We consider QCD $t\overline{t}\gamma$ and $t\overline{t}Z$ production at hadron colliders as a tool to measure the $tt\gamma$ and $ttZ$ couplings. At the Tevatron it may be possible to perform a first, albeit not very precise, test of the $tt\gamma$ vector and axial vector couplings in $t\overline{t}\gamma$ production, provided that more than $5{\mathrm{f}\mathrm{b}}^{-1}$ of integrated luminosity are accumulated. The $t\overline{t}Z$ cross section at the Tevatron is too small to be observable. At the CERN Large Hadron Collider (LHC) it will be possible to probe the $tt\gamma$ couplings at the few-percent level, which approaches the precision which one hopes to achieve with a next-generation $e^{+}{e}^{-}$ linear collider. The LHC’s capability of associated QCD $t\overline{t}V$ ($V=\gamma ,Z$) production has the added advantage that the $tt\gamma$ and $ttZ$ couplings are not entangled. For an integrated luminosity of $300{\mathrm{f}\mathrm{b}}^{-1}$, the $ttZ$ vector (axial vector) coupling can be determined with an uncertainty of $45-85\%$ ($15-20\%$), whereas the dimension-five dipole form factors can be measured with a precision of $50-55\%$. The achievable limits improve typically by a factor of $2-3$ for the luminosity-upgraded ($3{\mathrm{a}\mathrm{b}}^{-1}$) LHC.

As is known from previous studies the lepton number violating decays $K^{+}\to {\pi }^{-}+l_1^{+}+l_2^{+}$ have good prospects to probe new physics beyond the standard model and provide valuable information on neutrino masses and mixing. We analyze these processes with an emphasis on their hadronic structure aspects applying the relativistic constituent quark model. We conclude that the previously ignored contribution associated with the t-channel Majorana neutrino exchange is comparable with the s-channel one in a wide range of neutrino masses. We also estimate model independent absolute upper bounds on the neutrino contributions to these decays.

We study the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}\gamma$, with a hard photon radiated from the initial state. About 60 000 fully reconstructed events have been selected from $89{\mathrm{f}\mathrm{b}}^{-1}$ of BABAR data. The invariant mass of the hadronic final state defines the effective $e^{+}{e}^{-}$ $e^{+}{e}^{-}$ center-of-mass energy, so that these data can be compared with the corresponding direct $e^{+}{e}^{-}$ measurements. From the $4\pi$ -mass spectrum, the cross section for the process $e^{+}{e}^{-}$ $\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ is measured for center-of-mass energies from 0.6 to 4.5 $\mathrm{G}\mathrm{e}\mathrm{V}$. The uncertainty in the cross section measurement is typically 5%. We also measure the cross sections for the final states $K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}{K}^{+}{K}^{-}$. We observe the $J/\psi$ in all three final states and measure the corresponding branching fractions. We search for $X(3872)$ in $J/\psi (\to {\mu }^{+}{\mu }^{-}){\pi }^{+}{\pi }^{-}$ and obtain an upper limit on the product of the $e^{+}{e}^{-}$ width of the $X(3872)$ and the branching fraction for $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$.

We construct the most general couplings of a bulk seven-dimensional Yang-Mills-Einstein $\mathcal{N}=2$ supergravity with a boundary six-dimensional chiral $\mathcal{N}=(0,1)$ theory of vectors and charged hypermultiplets. The boundary consists of two brane worlds sitting at the fixed points of an ${\mathbf{S}}^1/{\mathbb{Z}}_2$ compactification of the seven-dimensional bulk supergravity. The resulting 6D massless spectrum surviving the orbifold projection is anomalous. By introducing boundary fields at the orbifold fixed points, we show that all anomalies are canceled by a Green-Schwarz mechanism. In addition, all couplings of the boundary fields to the bulk are completely specified by supersymmetry. We emphasize that there is no bulk Chern-Simons term to cancel the anomalies. The latter is traded for a Green-Schwarz term which emerges in the boundary theory after a duality transformation implemented to construct the bulk supergravity.

We study the decay of the cosmological constant in two spacetime dimensions through production of pairs. We show that the same nucleation process looks as quantum-mechanical tunneling (instanton) to one Killing observer and as thermal activation (thermalon) to another. Thus, we find another striking example of the deep interplay between gravity, thermodynamics and quantum mechanics which becomes apparent in presence of horizons.

We study gravitational perturbations in general braneworlds carrying a perturbation of the de Sitter universe. We derive our results from a full five-dimensional quantum field theory, and exhibit explicit formulas for the scalar and tensor power spectra. We show by explicit calculation that the dark radiation induced by our perturbation is zero, which implies that the deformation arises from the matter theory only and enables proper comparison with four-dimensional results. We argue that for the consistency relation to hold in the braneworld, significant fine tuning of the matter theory is necessary.

The nontrivial boundary conditions (BC’s) for the topcolor breaking are investigated in the context of the TeV-scale extra dimension scenario. In the gauge symmetry breaking mechanism via the BC’s we do not need to incorporate a dynamical mechanism for the topcolor breaking into the model. Moreover, the topcolor breaking can be realized without introducing explicitly a (composite) scalar field. We present a six dimensional model where the top and bottom quarks in the bulk have the topcolor charge while the other quarks in the bulk do not. We also put the electroweak gauge interaction in the six dimensional bulk. The bottom quark condensation is naturally suppressed owing to the powerlike running of the bulk $\mathrm{U}(1{)}_Y$ interaction, so that only the top condensation is expected to take place. We explore such a possibility based on the ladder Schwinger-Dyson equation and show the cutoff to make the model viable.

Models involving large extra spatial dimension(s) have interesting predictions on lepton flavor violating processes. We consider some five-dimensional (5D) models which are related to neutrino mass generation or address the fermion masses hierarchy problem. We study the signatures in low energy experiments that can discriminate the different models. The focus is on muon-electron conversion in nuclei $\mu \to e\gamma$ and $\mu \to 3e$ processes and their $\tau$ counterparts. Their links with the active neutrino mass matrix are investigated. We show that in the models we discussed the branching ratio of $\mu \to e\gamma$ like rare process is much smaller than the ones of $\mu \to 3e$ like processes. This is in sharp contrast to most of the traditional wisdom based on four-dimensional (4D) gauge models. Moreover, some rare tau decays are more promising than the rare muon decays.