The mass of the Higgs boson in the split-supersymmetric standard model is calculated, including all one-loop threshold effects and the renormalization group evolution of the Higgs quartic coupling through two-loops. The two-loop corrections are very small ($\ll 1\mathrm{GeV}$), while the one-loop threshold corrections generally push the Higgs mass down several GeV.

The cross section for ultrahigh energy neutrino-nucleon scattering is very sensitive to the parton distributions at very small values of Bjorken $x$ ($x\le {10}^{-4}$). We numerically investigate the effects of modifying the behavior of the gluon distribution function at very small $x$ in the DGLAP evolution equation. We then use the Color Glass Condensate formalism to calculate the neutrino-nucleon cross section at ultrahigh energies and compare the result with those based on modification of DGLAP evolution equation.

New arguments are presented in favor of the infrared-finite coupling approach to power corrections in the context of Sudakov resummation. The more regular infrared behavior of some peculiar combinations of Sudakov anomalous dimensions, free of Landau singularities at large $N_f$, is pointed out. A general conflict between the infrared-finite coupling and infrared renormalon approaches to power corrections is explained, and a possible resolution is proposed, which makes use of the arbitrariness of the choice of constant terms in the Sudakov exponent. Evidence for an infrared-finite perturbative effective coupling in the Drell-Yan process at large $N_f$ (albeit at odds with the infrared renormalon argument) is found within the framework of Sudakov resummation for eikonal cross sections of Laenen, Sterman and Vogelsang.

We study dynamics and radiation generation in the last few orbits and merger of a binary black hole system, applying recently developed techniques for simulations of moving black holes. Our analysis of the gravitational radiation waveforms and dynamical black hole trajectories produces a consistent picture for a set of simulations with black holes beginning on circular-orbit trajectories at a variety of initial separations. We find profound agreement at the level of 1% among the simulations for the last orbit, merger and ringdown. We are confident that this part of our waveform result accurately represents the predictions from Einstein’s General Relativity for the final burst of gravitational radiation resulting from the merger of an astrophysical system of equal-mass nonspinning black holes. The simulations result in a final black hole with spin parameter $a/m=0.69$. We also find good agreement at a level of roughly 10% for the radiation generated in the preceding few orbits.

We consider nonminimally coupled scalar fields to explore the Siklos spacetimes in three dimensions. Their interpretation as exact gravitational waves propagating on AdS space restrict the source to behave as a pure radiation field. We show that the related pure radiation constraints single out a unique self-interaction potential depending on one coupling constant. For a vanishing coupling constant, this potential reduces to a mass term with a mass fixed in terms of the nonminimal-coupling parameter. This mass dependence allows the existence of several free cases including massless and tachyonic sources. There even exists a particular value of the nonminimal-coupling parameter for which the corresponding mass exactly compensates the contribution generated by the negative scalar curvature, producing a genuinely massless field in this curved background. The self-interacting case is studied in detail for the conformal coupling. The resulting gravitational wave is formed by the superposition of the free and the self-interaction contributions, except for a critical value of the coupling constant where a nonperturbative effect relating the strong and weak regimes of the source appears. We establish a correspondence between the scalar source supporting an AdS wave and a pp wave by showing that their respective pure radiation constraints are conformally related, while their involved backgrounds are not. Finally, we consider the AdS waves for topologically massive gravity and its limit to conformal gravity.

In studies of high energy $pp$ and $\overline{p}p$ scattering, the odd (under crossing) forward scattering amplitude accounts for the difference between the $pp$ and $\overline{p}p$ cross sections. Typically, it is taken as $f_{-}=-\frac{p}{4\pi }D{s}^{\alpha -1}{e}^{i\pi (1-\alpha )/2}$ ($\alpha \sim 0.5$), which has $\Delta \sigma$, $\Delta \rho \to 0$ as $s\to \infty$, where $\rho$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. However, the odd-signatured amplitude can have in principle a strikingly different behavior, ranging from having $\Delta \sigma \to \mathrm{\text{nonzero constant}}$ to having $\Delta \sigma \to \ln s/s_0$ as $s\to \infty$, the maximal behavior allowed by analyticity and the Froissart bound. We reanalyze high energy $pp$ and $\overline{p}p$ scattering data, using new analyticity constraints, in order to put new and precise limits on the magnitude of “odderon” amplitudes.

In a previous paper (hep-th/0510080) the effective Landau-Lifshitz (LL) Lagrangians in the $SU(2)$ sector coming from string theory and gauge theory have been found to three loops in the effective expansion parameter $\tilde{\lambda }=\lambda /J^2$. In this paper we continue this study and find the effective Landau-Lifshitz Lagrangians to four loops. We extend to four-loops ${\tilde{\lambda }}^4$ the computations of $1/J$ and $1/J^2$ corrections to BMN energies done in hep-th/0510080 to three-loops. We compare these corrections obtained from quantum “gauge-theory” LL action with the corrections obtained from the conjectured Bethe ansatz for the long range spin chain representing perturbative large $N$ $\mathcal{N}=4$ Super Yang-Mills theory in the $SU(2)$ sector and find perfect matching to four loops ${\tilde{\lambda }}^4$. We compare also the $1/J$ and $1/J^2$ corrections obtained from quantum “string-theory” LL action with those obtained from the “quantum string” Bethe ansatz and again find perfect matching to four-loops.

We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schrödinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.

We discuss data analysis techniques that can be used in the search for gravitational wave bursts from cosmic strings. When data from multiple interferometers are available, we describe consistency checks that can be used to greatly reduce the false alarm rates. We construct an expression for the rate of bursts for arbitrary cosmic string loop distributions and apply it to simple known solutions. The cosmology is solved exactly and includes the effects of a late-time acceleration. We find substantially lower burst rates than previous estimates suggest and explain the disagreement. Initial LIGO is unlikely to detect field-theoretic cosmic strings with the usual loop sizes, though it may detect cosmic superstrings as well as cosmic strings and superstrings with nonstandard loop sizes (which may be more realistic). In the absence of a detection, we show how to set upper limits based on the loudest event. Using Initial LIGO sensitivity curves, we show that these upper limits may result in interesting constraints on the parameter space of theories that lead to the production of cosmic strings.

We rederive AdS/CFT predictions for infrared two-point functions by an entirely four-dimensional approach, without reference to holography. This approach, originally due to Migdal in the context of QCD, utilizes an extrapolation from the ultraviolet to the infrared using a Padé approximation of the two-point function. We show that the Padé approximation and AdS/CFT give the same leading order predictions, and we discuss including power corrections such as those due to condensates of gluons and quarks in QCD. At finite order the Padé approximation provides a gauge invariant regularization of a higher dimensional gauge theory in the spirit of deconstructed extra dimensions. The radial direction of anti-de Sitter space emerges naturally in this approach.

Semileptonic decays of heavy baryons consisting of one heavy ($Q=b$, $c$) and two light ($q=u$, $d$, $s$) quarks are considered in the heavy-quark-light-diquark approximation. The relativistic quasipotential equation is used for obtaining masses and wave functions of both diquarks and baryons within the constituent quark model. The weak transition matrix elements are expressed through the overlap integrals of the baryon wave functions. The Isgur-Wise functions are determined in the whole accessible kinematic range. The exclusive semileptonic decay rates and different asymmetries are calculated with applying the heavy quark $1/m_Q$ expansion. The evaluated ${\Lambda }_b\to {\Lambda }_{c}l\nu$ decay rate agrees with its experimental value.

We present the general formalism required to derive generalized parton distributions within a convolution model where the bare nucleon is dressed by its virtual meson cloud. In the one-meson approximation the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The baryon is assumed here to be either a nucleon or a $\Delta$ described within the constituent-quark model in terms of three-valence quarks; correspondingly, the meson, assumed to be a pion, is described as a quark-antiquark pair. Explicit expressions for the unpolarized generalized parton distributions are obtained and evaluated in different kinematics.

The galaxy image pair Capodimonte-Sternberg-Lens Candidate no. 1 (CSL-1) has been a leading candidate for a cosmic string lens. High quality imaging data from the Hubble Space Telescope presented here show that it is not a lens but a pair of galaxies. The galaxies show different orientations of their principal axes, not consistent with any lens model. We present a new direct test of the straight-string lens model, using a displaced difference of the image from itself to exclude CSL-1 at high confidence.

We derive a set of exact cosmological solutions to the $D=4$, $\mathcal{N}=1$ supergravity description of heterotic M theory. Having identified a new and exact $SU(3)$ Toda model solution, we then apply symmetry transformations to both this solution and to a previously known $SU(2)$ Toda model, in order to derive two further sets of new cosmological solutions. In the symmetry-transformed $SU(3)$ Toda case we find an unusual bouncing motion for the M5 brane, such that this brane can be made to reverse direction part way through its evolution. This bounce occurs purely through the interaction of nonstandard kinetic terms, as there are no explicit potentials in the action. We also present a perturbation calculation which demonstrates that, in a simple static limit, heterotic M theory possesses a scale-invariant isocurvature mode. This mode persists in certain asymptotic limits of all the solutions we have derived, including the bouncing solution.

An interesting case of string/black hole transition occurs in two-dimensional noncritical string theory dressed with a compact CFT. In these models the high energy densities of states of perturbative strings and black holes have the same leading behavior when the Hawking temperature of the black hole is equal to the Hagedorn temperature of perturbative strings. We compare the first subleading terms in the black hole and closed string entropies in this setting and argue that the entropy interpolates between these expressions as the energy is varied. We compute the subleading correction to the black hole entropy for a specific simple model.

We demonstrate that in $N=8$ supersymmetric mechanics with linear and nonlinear chiral supermultiplets one may dualize two auxiliary fields into physical ones in such a way that the bosonic manifold will be a hyper-Kähler one. The key point of our construction is about different dualizations of the two auxiliary components. One of them is turned into a physical one in the standard way through its replacement by the total time derivative of some physical field. The other auxiliary field which obeys the condition ${\partial }_t(\mathrm{Im}A+\mathrm{Im}B)=0$ is dualized through a Lagrange multiplier. We clarify this choice of dualization by presenting the analogy with a three-dimensional case.

Coupling constants of the vector meson nonet are determined in the large-$N_c$ limit, but beyond the chiral limit taking into account terms up to quadratic order in the Goldstone boson masses. With two input parameters five coupling constants for hadronic and dilepton decays are determined which agree very well with the experimental results. The obtained parameters are also used to calculate the pion and kaon decay constant in the large-$N_c$ limit. A consistent picture is only obtained, if the correct assignment of the $N_c$-dependence of the electromagnetic charges of the quarks is taken into account.

Defects in superfluid ${}^3\mathrm{He}$, high-$T_c$ superconductors, QCD color superfluids, and cosmic vortons can possess (anti)ferromagnetic cores, and theirgeneralizationss. In each case there is a second-order parameter whose value is zero in the bulk which does not vanish in the core. We examine the production of defects in the simplest $1+1$ dimensional scalar theory in which a second-order parameter can take nonzero values in a defect core. We study in detail the effects of core condensation on the defect production mechanism.

The evolution of multiple scalar fields in cosmology has been much studied, particularly when the potential is formed from a series of exponentials. For a certain subclass of such systems it is possible to get “assisted“ behavior, where the presence of multiple terms in the potential effectively makes it shallower than the individual terms indicate. It is also known that when compactifying on coset spaces one can achieve a consistent truncation to an effective theory which contains many exponential terms; however, if there are too many exponentials then exact scaling solutions do not exist. In this paper we study the potentials arising from such compactifications of eleven-dimensional supergravity and analyze the regions of parameter space which could lead to scaling behavior.

We study the phase space of the spherically symmetric solutions of Einstein-Maxwell-Gauss-Bonnet system nonminimally coupled to a scalar field and prove the existence of solutions with unusual asymptotics in addition to asymptotically flat ones. We also find new dyonic solutions of dilatonic Einstein-Maxwell theory.