The field equations associated with the Born-Infeld-Einstein action including matter are derived using a Palatini variational principle. Scalar, electromagnetic, and Dirac fields are considered. It is shown that an action can be chosen for the scalar field that produces field equations identical to the usual Einstein field equations minimally coupled to a scalar field. In the electromagnetic and Dirac cases the field equations reproduce the standard equations only to lowest order. The spherically symmetric electrovac equations are studied in detail. It is shown that the resulting Einstein equations correspond to gravity coupled to a modified Born-Infeld theory. It is also shown that the solution becomes singular on a spherical shell which implies that all charged particles must have a finite size. The space-time is therefore more singular than the Reissner-Nordström space-time, which is only singular at a point. Mass terms for the fields are also considered.

We show the existence of a pseudogap phase in the Nambu–Jona-Lasinio model of quark interactions. In the pseudogap phase chiral symmetry is restored but $q\overline{q}$ pseudoscalar mesons still exist and they are massive. Such a behavior is intermediate between a BCS superconductor and a Bose-Einstein Condensate. We suggest the relevance of this phenomenon for an understanding of recent lattice QCD and experimental data.

We investigate QCD effects in the production of a single slepton at hadron colliders in the minimal supersymmetric standard model without $R$ parity. We calculate the total cross sections and the transverse momentum distributions at next-to-leading order in QCD. The next-to-leading-order corrections enhance the total cross sections and decrease the dependence of the total cross sections on the factorization and renormalization scales. For the differential cross sections, we resum all-order soft gluon effects to give reliable predictions for the transverse momentum distributions. We also compare two approaches to the nonperturbative parametrization and found that the results are slightly different at the Tevatron and are in good agreement at the Large Hadron Collider. Our results can be useful to the simulation of the events and to the future collider experiments.

The nonextreme $Dp$-brane solutions in type II supergravity (in the near-horizon limit) are expected to be dual to $(p+1)$-dimensional noncompact supersymmetric Yang-Mills theories at finite temperature. We study the translationally invariant perturbations along the branes in those backgrounds and calculate quasinormal frequencies numerically. These frequencies should determine the thermalization time scales in the dual Yang-Mills theories.

We introduce and study in some detail the properties of a novel class of Weyl-conformally invariant $p$-brane theories which describe intrinsically lightlike branes for any odd world-volume dimension. Their dynamics significantly differs from that of the ordinary (conformally noninvariant) Nambu-Goto $p$ branes. We present explicit solutions of the Weyl-invariant lightlike brane- (WILL-brane) equations of motion in various gravitational models of physical relevance exhibiting various new phenomena. In $D=4$ the WILL membrane serves as a material and charged source for gravity and electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it automatically positions itself on (straddles) the common event horizon of the corresponding matching black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics. In product spaces of interest in Kaluza-Klein theories the WILL-brane wraps nontrivially around the compact (internal) dimensions and still describes massless mode dynamics in the noncompact (space-time) dimensions. Because of nontrivial variable size of the internal compact dimensions we find new types of physically interesting solutions describing massless brane modes trapped on bounded planar circular orbits with nontrivial angular momentum, and with linear dependence between energy and angular momentum.

We present a systematic method for constructing consistent interactions for a tensor field of an arbitrary rank in the adjoint representation of an arbitrary gauge group in any space-time dimensions. This method is inspired by the dimensional reduction of Scherk-Schwarz, modifying field strengths with certain Chern-Simons forms, together with modified tensorial gauge transformations. In order to define a consistent field strength of a $r$-rank tensor $B_{{\mu }_1\cdots {\mu }_r}{}^I$ in the adjoint representation, we need the multiplet ($B_{{\mu }_1\cdots {\mu }_r}{}^I$, $B_{{\mu }_1\cdots {\mu }_{r-1}}{}^{IJ}$, $\cdots$, $B_{\mu }{}^{I_1\cdots I_r}$, $B^{I_1\cdots I_{r+1}}$). The usual problem of consistency of the tensor field equations is circumvented in this formulation.

The most promising way to compute the gravitational waves emitted by binary black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques fail, is a quasistationary approximation introduced by Detweiler and being pursued by Price and others. In this approximation the outgoing gravitational waves at infinity and downgoing gravitational waves at the holes’ horizons are replaced by standing waves so as to guarantee that the spacetime has a helical Killing vector field. Because the horizon generators will not, in general, be tidally locked to the holes’ orbital motion, the standing waves will destroy the horizons, converting the black holes into naked singularities that resemble black holes down to near the horizon radius. This paper uses a spherically symmetric, scalar-field model problem to explore in detail the following BBH issues: (i) The destruction of a horizon by the standing waves. (ii) The accuracy with which the resulting naked singularity resembles a black hole. (iii) The conversion of the standing-wave spacetime (with a destroyed horizon) into a spacetime with downgoing waves by the addition of a “radiation-reaction field.” (iv) The accuracy with which the resulting downgoing waves agree with the downgoing waves of a true black-hole spacetime (with horizon). The model problem used to study these issues consists of a Schwarzschild black hole endowed with spherical standing waves of a scalar field, whose wave frequency and near-horizon energy density are chosen to match those of the standing gravitational waves of the BBH quasistationary approximation. It is found that the spacetime metric of the singular, standing-wave spacetime, and its radiation-reaction-field-constructed downgoing waves are quite close to those for a Schwarzschild black hole with downgoing waves—sufficiently close to make the BBH quasistationary approximation look promising for non-tidally-locked black holes.

The metric of a Schwarzschild solution in brane induced gravity in five dimensions is studied. We find a nonperturbative solution for which an exact expression on the brane is obtained. We also find a linearized solution in the bulk and argue that a nonsingular exact solution in the entire space should exist. The exact solution on the brane is highly nontrivial as it interpolates between different distance scales. This part of the metric is enough to deduce an important property—the Arnowitt-Deser-Misner canonical formalism (ADM) mass of the solution is suppressed compared to the bare mass of a static source. This screening of the mass is due to nonlinear interactions which give rise to a nonzero curvature outside the source. The curvature extends away from the source to a certain macroscopic distance that coincides with the would-be strong interaction scale. The very same curvature shields the source from strong coupling effects. The four-dimensional law of gravity, including the correct tensorial structure, is recovered at observable distances. We find that the solution has no van Dam-Veltman-Zakharov discontinuity and show that the gravitational field on the brane is always weak, in spite of the fact that the solution is nonperturbative.

The general endpoint of the $rp$ process in rapidly accreting neutron stars is believed to be a surface distribution of matter whose nuclear composition may depend on position. Its evolution during compression beyond the neutron-drip threshold density ${\rho }_{nd}$ is determined by the presence of nuclear formation enthalpy minima at the proton closed shells. At ${\rho }_{nd}$, a sequence of weak interactions with capture or emission of neutron pairs rapidly transform nuclei to the most accessible proton closed shell. Therefore, angular asymmetries in nuclear composition present in accreted matter at ${\rho }_{nd}$ are preserved during further compression toward densities $\sim {10}^{14}\mathrm{g}{\mathrm{cm}}^{-3}$ provided transition rates between closed shells are negligible. Although it has been confirmed that this condition is satisfied for predicted internal temperatures and for the formation enthalpy distribution used in this work, it would not be so if the true enthalpy differences between maxima and minima in the distribution were a factor of 2 smaller. For this reason, it does not appear possible to assert with any confidence that position-dependent surface composition can lead to significant angle-dependence of the equation of state and to potentially observable gravitational radiation. The effect of nonradial internal temperature gradients on angle-dependency of the equation of state is also not quantifiable.

We use data from the second science run of the LIGO gravitational-wave detectors to search for the gravitational waves from primordial black hole binary coalescence with component masses in the range $0.2–1.0M_{\odot }$. The analysis requires a signal to be found in the data from both LIGO observatories, according to a set of coincidence criteria. No inspiral signals were found. Assuming a spherical halo with core radius 5 kpc extending to 50 kpc containing nonspinning black holes with masses in the range $0.2–1.0M_{\odot }$, we place an observational upper limit on the rate of primordial black hole coalescence of 63 per year per Milky Way halo (MWH) with 90% confidence.

We use 373 hours ($\approx 15$ days) of data from the second science run of the LIGO gravitational-wave detectors to search for signals from binary neutron star coalescences within a maximum distance of about 1.5 Mpc, a volume of space which includes the Andromeda Galaxy and other galaxies of the Local Group of galaxies. This analysis requires a signal to be found in data from detectors at the two LIGO sites, according to a set of coincidence criteria. The background (accidental coincidence rate) is determined from the data and is used to judge the significance of event candidates. No inspiral gravitational-wave events were identified in our search. Using a population model which includes the Local Group, we establish an upper limit of less than 47 inspiral events per year per Milky Way equivalent galaxy with 90% confidence for nonspinning binary neutron star systems with component masses between 1 and $3M_{\odot }$.

We compute $\mathcal{O}({\alpha }_s)$ lattice-to-continuum perturbative matching coefficients for the $\Delta S=2$ flavor changing four-quark operators for the Asqtad improved staggered action. In conjunction with lattice simulations with three flavors of light, dynamical quarks, our results yield an unquenched determination of $B_K$, the parameter that determines the amount of indirect $CP$ violation in the neutral kaon system. Its value is an important input for the unitarity triangle analysis of weak decays.

Based on a new, exact QCD factorization formula for the partial $\overline{B}\to X_s\gamma$ decay rate with a restriction on large photon energy, improved predictions are presented for the partial moments $⟨E_{\gamma }⟩$ and $⟨E_{\gamma }^2⟩-⟨E_{\gamma }{⟩}^2$ of the photon spectrum defined with a cut $E_{\gamma }\ge E_0$. In the region where $\Delta =m_b-2E_0$ is large compared with ${\Lambda }_{\mathrm{QCD}}$, a theoretical description without recourse to shape functions can be obtained. However, for $\Delta \ll m_b$ it is important to separate short-distance contributions arising from different scales. The leading terms in the heavy-quark expansion of the moments receive contributions from the scales $\Delta$ and $\sqrt{m_b\Delta }$ only, but not from the hard scale $m_b$. For these terms, a complete scale separation is achieved at next-to-next-to-leading order in renormalization-group improved perturbation theory, including two-loop matching contributions and three-loop running. The results presented here can be used to extract the $b$-quark mass and the quantity ${\mu }_{\pi }^2$ with excellent theoretical precision. A fit to experimental data reported by the Belle Collaboration yields $m_b^{\mathrm{SF}}=(4.62\pm {0.10}_{\exp }\pm {0.03}_{\mathrm{th}})\mathrm{GeV}$ and ${\mu }_{\pi }^{2,\mathrm{SF}}=(0.11\pm {0.19}_{\exp }\pm {0.08}_{\mathrm{th}}){\mathrm{GeV}}^2$ in the shape-function scheme at a scale ${\mu }_f=1.5\mathrm{GeV}$, while $m_b^{\mathrm{kin}}=(4.54\pm {0.11}_{\exp }\pm {0.04}_{\mathrm{th}})\mathrm{GeV}$ and ${\mu }_{\pi }^{2,\mathrm{kin}}=(0.49\pm {0.18}_{\exp }\pm {0.09}_{\mathrm{th}}){\mathrm{GeV}}^2$ in the kinetic scheme at a scale ${\mu }_f=1\mathrm{GeV}$.

We calculate $m_{ud}=(m_u+m_d)/2$, $m_s$, $f_{\pi }$ and $f_K$ in the quenched continuum limit with UV-filtered overlap fermions. We see rather small scaling violations on lattices as coarse as $a^{-1}\simeq 1\mathrm{GeV}$ and conjecture that similar advantages would be manifest in unquenched studies.

We give a quantum field theoretical derivation of the scalar Abraham-Lorentz-Dirac (ALD) equation and the self-force for a scalar charged particle interacting with a quantum scalar field in curved spacetime. We regularize the causal Green’s function using a quasilocal expansion in the spirit of effective field theory and obtain a regular expression for the self-force. The scalar ALD equation obtained in this way for the classical motion of the particle checks with the equation obtained by Quinn earlier [T. C. Quinn, Phys. Rev. D 62, 064029 (2000).]. We further derive a scalar ALD-Langevin equation with a classical stochastic force accounting for the effect of quantum fluctuations in the field, which causes small fluctuations on the particle trajectory. This equation will be useful for the study of stochastic motion of charges under the influence of both quantum and classical noise sources, derived either self-consistently (as done here) or put in by hand (with warnings). We show the possibility of secular effects from such stochastic influences on the trajectory that may impact on the present calculations of gravitational waveform templates.

We present a fourth-order convergent, $(2+1)$-dimensional, numerical formalism to solve the Teukolsky equation in the time domain. Our approach is first to rewrite the Teukolsky equation as a system of first-order differential equations. In this way we get a system that has the form of an advection equation. This is then used in combination with a series expansion of the solution in powers of time. To obtain a fourth-order scheme we kept terms up to fourth derivative in time and use the advectionlike system of differential equations to substitute the temporal derivatives by spatial derivatives. This scheme is applied to evolve gravitational perturbations in the Schwarzschild and Kerr backgrounds. Our numerical method proved to be stable and fourth-order convergent in $r^{*}$ and $\theta$ directions. The correct power-law tail, $\sim 1/t^{2\ell +3}$, for general initial data, and $\sim 1/t^{2\ell +4}$, for time-symmetric data, was found in our runs. We noted that it is crucial to resolve accurately the angular dependence of the mode at late times in order to obtain these values of the exponents in the power-law decay. In other cases, when the decay was too fast and round-off error was reached before a tail was developed, then the quasinormal modes frequencies provided a test to determine the validity of our code.

We investigate the Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field governed by the non-Abelian Born-Infeld action. A similar system with the standard Einstein-Yang-Mills (EYM) action is known to exhibit chaotic behavior induced by the Yang-Mills field. When the action is replaced by the Born-Infeld–type non-Abelian action (NBI), the chaos-order transition is observed in the high-energy region. This is interpreted as a smothering effect due to (nonperturbative in ${\alpha }^{\prime }$) string corrections to the classical EYM action. We give numerical evidence for the chaos-order transition and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld nonlinearity. We also perform a general analysis of the Bianchi I NBI cosmology and derive an exact solution in the case of only the U(1) component excited. Our new exact solution generalizes the Rosen solution of the Bianchi I Einstein-Maxwell cosmology to the U(1) Einstein-Born-Infeld theory.

The $CP$ asymmetry in the $B\to K_S{K}_S{K}_S$ decay is being measured by the two $B$ factories. A large deviation of the $CP$ asymmetry $S_{K_S{K}_S{K}_S}$ from $-S_{\psi K_S}$ and/or of $C_{K_S{K}_S{K}_S}$ from zero would imply new physics in $b\to s$ transitions. We try to put upper bounds on the Standard Model size of these deviations, using SU(3) flavor relations and experimental data on the branching ratios of various decay modes that proceed via $b\to d$ transitions. We point out several subtleties that distinguish the case of three-body final states from two body ones. We present several simple relations that can become useful once all relevant modes are measured accurately enough.

The Standard Model Extension formulated by Colladay and Kostelecký is reviewed in the framework of the ${}^{4}He$ primordial abundance. Upper bounds on coefficients for the Lorentz violation are derived using the present observational data.

We construct the general $1/2$ BPS M2 giant graviton solutions asymptotic to the 11-dimensional maximally supersymmetric plane-wave background, based on the recent work of Lin, Lunin, and Maldacena. The solutions have null singularity and we argue that it is unavoidable to have null singularity in the proposed framework, although the solutions are still physically relevant. They involve an arbitrary function $F(x)$ which is shown to have a correspondence to the $1/2$ BPS states of the Berenstein-Maldacena-Nastase (BMN) matrix model. A detailed map between the $1/2$ BPS states of both sides is worked out.