We propose that the extrinsic curvature and torsion of a bosonic string can be employed as Hamiltonian variables in a two dimensional Landau-Ginzburg gauge field theory. Their interpretation in terms of the Abelian Higgs multiplet leads to two different phases. In the phase with unbroken gauge symmetry the ground state describes open strings while in the phase with broken gauge symmetry the ground state involves closed strings. Finally, we relate aspects of the extrinsic geometry to the spectral properties of a Dirac operator, minimally coupled to the Abelian Higgs multiplet.

We analyze the structure of supersymmetric Gödel-like cosmological solutions of string theory. Just as the original four-dimensional Gödel universe, these solutions represent rotating, topologically trivial cosmologies with a homogeneous metric and closed timelike curves. First we focus on the “phenomenological” aspects of holography, and identify the preferred holographic screens associated with inertial comoving observers in Gödel universes. We find that holography can serve as a chronology protection agency: The closed timelike curves are either hidden behind the holographic screen, or broken by it into causal pieces. In fact, holography in Gödel universes has many features in common with de Sitter space, suggesting that Gödel universes could represent a supersymmetric laboratory for addressing the conceptual puzzles of de Sitter holography. Then we initiate the investigation of “microscopic” aspects of holography of Gödel universes in string theory. We show that Gödel universes are T dual to pp waves, and use this fact to generate new Gödel-like solutions of string and M theory by T dualizing known supersymmetric pp-wave solutions.

A class of exact solutions of the Skyrme model is obtained. The solutions are described by the Weierstrass $\wp$ function or the Jacobi elliptic function. They are not solitonic but of wave character. They supply us with examples of the superposition of three plane waves in the Skyrme model.

The free energy density, or pressure, of QCD has at high temperatures an expansion in the coupling constant g, known so far up to order $g^5.$ We compute here the last contribution which can be determined perturbatively, $g^6\ln \mathrm{}(1/g),$ by summing together results for the 4-loop vacuum energy densities of two different three-dimensional effective field theories. We also demonstrate that the inclusion of the new perturbative $g^6\ln \mathrm{}(1/g)\mathrm{}$ terms, once they are summed together with the so far unknown perturbative and nonperturbative $g^6$ terms, could potentially extend the applicability of the coupling constant series down to surprisingly low temperatures.

We argue that in the pure $\mathcal{N}=1\mathrm{}$ super Yang-Mills theory gauge symmetry is spontaneously broken to the maximal Abelian subgroup. In particular, the colored gluino condensate is nonzero. It invalidates, in a subtle way, the so-called strong-coupling instanton calculation of the (normal) gluino condensate and resolves the long-standing paradox of why its value does not agree with that obtained by other methods.

We study the five-dimensional Einstein-Yang-Mills system with a cosmological constant. Assuming a spherically symmetric spacetime, we find a new analytic black hole solution, which approaches asymptotically “quasi-Minkowski,” “quasi–anti-de Sitter,” or “quasi–de Sitter” spacetime depending on the sign of the cosmological constant. Since there is no singularity except for the origin that is covered by an event horizon, we regard it as a localized object. This solution corresponds to a magnetically charged black hole. We also present a singularity-free particlelike solution and a nontrivial black hole solution numerically. Those solutions correspond to the Bartnik-McKinnon solution and a colored black hole with a cosmological constant in four dimensions. We analyze their asymptotic behavior, spacetime structures, and thermodynamical properties. We show that there is a set of stable solutions if the cosmological constant is negative.

We discuss the effective theory for the close limit of two branes in a covariant way. To do so we solve the five-dimensional Einstein equation along the direction of the extra dimension. Using the Taylor expansion we solve the bulk spacetimes and derive the effective theory describing the close limit. We also discuss the radion dynamics and braneworld black holes for the close limit in our formulation.

We present the complete numerical method of general relativistic magnetohydrodynamic simulations in Kerr space-time, and then apply those techniques to the basic astrophysical problem of activity near a Kerr black hole immersed in a plasma with a large-scale magnetic field. Our numerical results show that a torsional Alfven wave is generated in the ergosphere of the Kerr black hole. This wave propagates outward along the magnetic field lines, extracting rotational energy from the plasma in the ergosphere. If the magnetic field is strong enough, the plasma energy in the ergosphere rapidly decreases and eventually becomes negative. When this negative energy plasma is swallowed by the black hole, the total energy of the black hole decreases, spinning it down. This energy extraction mechanism is similar to the “Penrose process,” in which the negative energy also plays an important role. The difference between the two is the force that causes the redistribution of the angular momentum (which is necessary to produce the negative energy). In the Penrose process, elementary particle interactions cause the redistribution, while in the present case it is performed by magnetic tension.

We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time and find that dimensional regularization is a manifestly supersymmetric regularization scheme, since the classically supersymmetric action does not need any counterterm to preserve worldline supersymmetry. We apply this regularization scheme to the worldline description of Dirac fermions coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4 dimensions, providing an additional check on the regularization with finite propagation time. Then we come to the main topic and consider the one-loop effective action for a Dirac field in a gravitational background. We describe how to represent this effective action as a worldline path integral and compute explicitly the one- and two-point correlation functions, i.e. the spin 1/2 particle contribution to the graviton tadpole and graviton self-energy. These results are presented for the general case of a massive fermion. It is interesting to note that in the worldline formalism the coupling to gravity can be described entirely in terms of the metric, avoiding the introduction of a vielbein. Consequently, the fermion-graviton vertices are always linear in the graviton, just like the standard coupling of fermions to gauge fields.

The maximal signal and peak of high-frequency relic gravitational waves (GW’s), recently predicted by quintessential inflationary models, may be firmly localized in the gigahertz region; the energy density of the relic gravitons in critical units (i.e., $h_0^2{\Omega }_{\mathrm{GW}})$ is of the order of ${10}^{-6},$ roughly eight orders of magnitude larger than in ordinary inflationary models. This is just the best frequency band for the electromagnetic (e.m.) response to high-frequency GW’s in smaller e.m. detecting systems. We consider the e.m. response of a Gaussian beam passing through a static magnetic field to a high-frequency relic GW. It is found that under the synchroresonance condition the first-order perturbative e.m. power fluxes will contain a “left circular wave” and a “right circular wave” around the symmetrical axis of the Gaussian beam, but the perturbative effects produced by the states of + polarization and $\times$ polarization of the relic GW have different properties, and the perturbations of their behavior are obviously different from those of the background e.m. fields in the local regions. For a high-frequency relic GW with the typical parameters ${\nu }_g{=10\mathrm{}}^{10}\mathrm{Hz},{h=10\mathrm{}}^{-30}$ in quintessential inflationary models, the corresponding perturbative photon flux passing through a region of ${10}^{-2}{\mathrm{m}}^2$ would be expected to be ${10}^3{\mathrm{s}}^{-1}.$ This is the largest perturbative photon flux we recently analyzed and estimated using the typical laboratory parameters. In addition, we also discuss the geometrical phase shift generated by high-frequency relic GW’s in the Gaussian beam and estimate possible physical effects.

We compare the sensitivity of WIMP detection via direct separation of possible signal versus background to WIMP detection via detection of an annual modulation, in which signal and background cannot be separated on an event-by-event basis. In order to determine how the constraints from the two different types of experiments might be combined an adequate incorporation of uncertainties due to galactic halo models must be made. This issue is particularly timely in light of recent direct detection limits from Edelweiss and CDMS, which we now demonstrate cannot be made consistent with the most recent claimed DAMA annual modulation observation by including halo uncertainties for spin independent interactions. On the other hand, we demonstrate that a combination of these two techniques, in the event of any positive direct detection signal, could ultimately allow significant constraints on anisotropic halo models even without directional sensitivity in these detectors.

The problems of attempting inflationary model building in a theory containing a dilaton are explained. In particular, I study the shape of the dilaton potential today and during inflation, based on a weakly coupled heterotic string model where corrections to the Kähler potential are assumed to be responsible for dilaton stabilization. Although no specific model building is attempted, if the inflationary energy density is related to the scale of gaugino condensation, then the dilaton may be stabilized close enough to today’s value that there is no significant change in the grand unified theory scale coupling. This can occur in a very wide range of models, and helps to provide some justification for the standard predictions of the spectral index. I explain how this result can ultimately be traced to the supersymmetry structure of the theory.

We consider a scenario in which our observable universe is a 3-dimensional surface (3-brane) living in extra dimensions with a warped geometry. We explore the interesting possibility that “lensed” density perturbations from other branes may serve as possible seeds for structure formation on our observable brane (without inflation), and, in addition, provide constraints on braneworld scenarios with warped bulk geometry. Because of the warped bulk metric, any perturbation generated on one brane (or in the bulk matter) appears to an observer on a second brane to have a significantly different amplitude. We analyze lensed perturbations in the Randall-Sundrum type scenarios and the “shortcut metric” scenarios. For Lorentz violating metrics in the bulk, we find the attractive possibility that large density fluctuations that are causally produced elsewhere can lead to small density fluctuations on our brane on superhorizon (acausal) length scales, as required by structure formation. Our most interesting result is that the “shortcut metrics” in which geodesics traverse the extra dimensions has the chance of providing an alternative to inflation with two important features: a possible solution to the horizon problem and a possible mechanism to generate large scale perturbations necessary for structure formation.

I present a method for accurately calculating the pole mass of the lightest Higgs scalar boson in supersymmetric extensions of the standard model, using a mass-independent renormalization scheme. The Higgs scalar self-energies are approximated by supplementing the exact one-loop results with the second derivatives of the complete two-loop effective potential in Landau gauge. I discuss the dependence of this approximation on the choice of renormalization scale, and note the existence of particularly poor choices, which fortunately can be easily identified and avoided. For typical input parameters, the variation in the calculated Higgs boson mass over a wide range of renormalization scales is found to be of the order of a few hundred MeV or less, and is significantly improved over previous approximations.

A mechanism is proposed in which a right-handed neutrino zero mode and a right-handed charged lepton zero mode can be localized at the same place along an extra compact dimension while having markedly different spreads in their wave functions: a relatively narrow one for the neutrino and a rather broad one for the charged lepton. In their overlaps with the wave function for the left-handed zero modes, this mechanism could produce a natural large hierarchy in the effective Yukawa couplings in four dimensions, and hence a large disparity in masses.

We consider the lightest Kaluza-Klein particles at the $N=1\mathrm{}$ mode (LKP) of universal extra dimensions to be a candidate for cold dark matter. We discuss the possibility of detecting them through direct detection at earth bound detectors. The detection rates for such particles are predicted for germenium, NaI, and xenon detectors. We have also calculated the nature of annual modulation for the dark matter signals in these detectors for the case of LKP dark matter. The variation of detection rates with the variation of rotational speed of the Solar System in the galactic rest frame is also addressed.

We study the locality and topological properties of fat link clover overlap (FCO) actions. We find that a small amount of fattening already results in greatly improved properties compared to the Wilson overlap (WO). We present a detailed study of the localization of the FCO and its connection to the density of low modes of $A^{†}A.\mathrm{}$ In contrast with the Wilson overlap, on quenched gauge backgrounds we do not find any dependence of the localization of the FCO on the gauge coupling. This suggests that the FCO remains local in the continuum limit. The FCO also faithfully reproduces the zero mode wave functions of typical lattice instantons, not like the Wilson overlap. After a general discussion of different lattice definitions of the topological charge we also show that the FCO together with the Boulder charge are likely to satisfy the index theorem in the continuum limit. Finally, we present a high statistics computation of the quenched topological susceptibility with the FCO action.

The pion electromagnetic form factor with leading and next-to-leading twist corrections is studied in the framework of the pQCD approach. We find that the Sudakov effects provide a weak suppression of the nonperturbative contributions at the experimental accessible energy region. We also find a large twist-3 contribution. Our conclusion is that the prediction of the pion form factor in the pQCD approach is not precise.

We report a measurement of the $B^0-B^0$ mixing parameter $\Delta m_d$ based on a $29.1{\mathrm{fb}}^{-1}$ sample of ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance decays collected by the Belle detector at the KEKB asymmetric $e^{+}{e}^{-}$ collider. We use events with a partially reconstructed $B^0\left(B^0\right)\to D^{*\mp }{\pi }^{\pm }$ candidate and where the flavor of the accompanying B meson is identified by the charge of the lepton from a $B^0\left(B^0\right)\to X^{\mp }{\mathcal{l}}^{\pm }\nu$ decay. The proper-time difference between the two B mesons is determined from the distance between the two decay vertices. From a simultaneous fit to the proper-time distributions for the same-flavor $\left(B^0\right(B^0),{\mathcal{l}}^{\pm })$ and opposite-flavor $\left(B^0\right(B^0),{\mathcal{l}}^{\mp })$ event samples, we measure the mass difference between the two mass eigenstates of the neutral B meson to be $\Delta m_d=(0.509\pm 0.017(\mathrm{stat})\pm 0.020(\mathrm{syst}\left)\right){\mathrm{ps}}^{-1}.$

We present a numerical study of the gluon propagator in the lattice Landau gauge for three-dimensional pure $\mathrm{SU}\left(2\right)\mathrm{}$ lattice gauge theory at couplings $\beta =4.2,$ 5.0, 6.0 and for lattice volumes ${V=40\mathrm{}}^3,$ ${80}^3,$ ${140}^3.$ In the limit of large $V$ we observe a decreasing gluon propagator for momenta smaller than $p_{\mathrm{dec}}{=350\mathrm{}}_{-50}^{+100\mathrm{}}\mathrm{MeV}.$ Data are well fitted by Gribov-like formulas and seem to indicate an infrared critical exponent κ slightly above 0.6, in agreement with recent analytic results.