BSSN-type evolution equations are discussed. The name refers to the Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution equations, without introducing the conformal-traceless decomposition but keeping the three connection functions and including a densitized lapse. It is proved that a pseudodifferential first order reduction of these equations is strongly hyperbolic. In the same way, densitized Arnowitt-Deser-Misner evolution equations are found to be weakly hyperbolic. In both cases, the positive densitized lapse function and the spacelike shift vector are arbitrary given fields. This first order pseudodifferential reduction adds no extra equations to the system and so no extra constraints.

We show that even in the simple framework of pure Kaluza-Klein gravity the shape moduli can generate potentials supporting inflation and/or quintessence. Using the shape moduli as the inflaton or quintessence field has the additional benefit of being able to explain symmetry breaking in a natural geometric way. A numerical analysis suggests that in these models it may be possible to obtain sufficient e-foldings during inflation as well as a small cosmological constant at the current epoch (without fine-tuning), while preserving the constraint coming from the fine structure constant.

Using some simple toy models, we explore the nature of the brane-bulk interaction for cosmological models with a large extra dimension. We are in particular interested in understanding the role of the bulk gravitons, which from the point of view of an observer on the brane will appear to generate dissipation and nonlocality, effects that cannot be incorporated into an effective (3+1)-dimensional Lagrangian field theoretic description. We explicitly work out the dynamics of several discrete systems consisting of a finite number of degrees of freedom on the boundary coupled to a (1+1)-dimensional field theory subject to a variety of wave equations. Systems both with and without time translation invariance are considered and moving boundaries are discussed as well. The models considered contain all the qualitative features of quantized linearized cosmological perturbations for a Randall-Sundrum universe having an arbitrary expansion history, with the sole exception of gravitational gauge invariance, which will be treated in a later paper.

We present a phenomenological study of top squarks $\left(t_{1,2}\right)$ and bottom squarks $\left(b_{1,2}\right)$ in the minimal supersymmetric standard model (MSSM) with complex parameters $A_t,A_b,\mu ,$ and $M_1.$ In particular we focus on the CP phase dependence of the branching ratios of $t_{1,2}$ and $b_{1,2}$ decays. We give the formulas of the two-body decay widths and present numerical results. We find that the effect of the phases on the $t_{1,2}$ and $b_{1,2}$ decays can be quite significant in a large region of the MSSM parameter space. This could have important implications for $t_{1,2}$ and $b_{1,2}$ searches and the MSSM parameter determination in future collider experiments. We have also estimated the accuracy expected in the determination of the parameters of $t_i$ and $b_i$ by a global fit of the measured masses, decay branching ratios, and production cross sections at $e^{+}{e}^{-}$ linear colliders with polarized beams. Analyzing two scenarios, we find that the fundamental parameters apart from $A_t$ and $A_b$ can be determined with errors of 1% to 2%, assuming an integrated luminosity of $1{\mathrm{ab}}^{-1}$ and a sufficiently large center of mass system (c.m.s.) energy to produce also the heavier $t_2$ and $b_2$ states. The parameter $A_t$ can be determined with an error of 2–3%, whereas the error on $A_b$ is likely to be of the order of 50%.

We report on a nonperturbative evaluation of the renormalization factors for the vector and axial-vector currents, $Z_V$ and $Z_A,$ in the quenched domain-wall QCD (DWQCD) with plaquette and renormalization-group-improved gauge actions. We take the Dirichlet boundary condition for both gauge and domain-wall fermion fields on the finite box, and introduce flavor-chiral Ward-Takahashi identities to calculate the renormalization factors. As a test of the method, we numerically confirm the expected relation that $Z_V\simeq Z_A$ in DWQCD. Employing two different box sizes for the numerical simulations at several values of the gauge coupling constant $g^2$ and the domain-wall height M, we extrapolate $Z_V$ to infinite volume to remove $a/L$ errors. We finally give the interpolation formula of $Z_V$ in the infinite volume as a function of $g^2$ and M.

I describe a subtraction scheme for the next-to-next-to-leading order calculation of single inclusive production at hadron colliders. Such processes include Drell-Yan, $W^{\pm },$ Z and Higgs Boson production. The key to such a calculation is a treatment of initial state radiation which preserves the production characteristics, such as the rapidity distribution, of the process involved. The method builds upon the Dipole Formalism and, with proper modifications, could be applied to deep inelastic scattering and $e^{+}{e}^{-}$ annihilation to hadrons.

Critical collapse of a self-gravitating scalar field in a (2+1)-dimensional spacetime with negative cosmological constant seems to be dominated by a continuously self-similar solution of the field equations without cosmological constant. However, previous studies of linear perturbations in this background were inconclusive. We extend the continuously self-similar solutions to solutions of the field equations with negative cosmological constant, and analyze their linear perturbations. The extended solutions are characterized by a continuous parameter. A suitable choice of this parameter seems to improve the agreement with the numerical results. We also study the dynamics of the apparent horizon in the extended background.

In order to discuss the well-posed initial value formulation of the teleparallel gravity and apply it to numerical relativity a symmetric hyperbolic system in the self-dual teleparallel gravity, which is equivalent to the Ashtekar formulation, is posed. This system is different from the ones in other works by that the reality condition of the spatial metric is included in the symmetric hyperbolicity and then is no longer an independent condition. In addition the constraint equations of this system are rather simpler than the ones in other works.

A general formalism for the dynamics of nonrotating cylindrical thin-shell wormholes is developed. The time evolution of the throat is explicitly obtained for thin-shell wormholes whose metric has the form associated with local cosmic strings. It is found that the throat collapses to zero radius, remains static, or expands forever, depending only on the sign of its initial velocity.

We use the cosmic microwave background angular power spectra to place upper limits on the degree to which global defects may have aided cosmic structure formation. We explore this under the inflationary paradigm, but with the addition of textures resulting from the breaking of a global $O\left(4\right)\mathrm{}$ symmetry during the early stages of the Universe. As a measure of their contribution, we use the fraction of the temperature power spectrum that is attributed to the defects at a multipole of 10. However, we find a parameter degeneracy enabling a fit to the first-year WMAP data to be made even with a significant defect fraction. This degeneracy involves the baryon fraction and the Hubble constant, plus the normalization and tilt of the primordial power spectrum. Hence, constraints on these cosmological parameters are weakened. Combining the WMAP data with a constraint on the physical baryon fraction from big bang nucleosynthesis calculations and high-redshift deuterium abundance limits the extent of the degeneracy and gives an upper bound on the defect fraction of 0.13 (95% confidence).

The quenched chiral logarithms are examined on a ${16}^3\times 28$ lattice with Iwasaki gauge action and overlap fermions. The pion decay constant $f_{\pi }$ is used to set the lattice spacing, $a=0.200\mathrm{}\left(3\right)\mathrm{}\mathrm{fm}.$ With pion mass as low as $\sim 180\mathrm{MeV},$ we see the quenched chiral logarithms clearly in $m_{\pi }^2/m$ and $f_P,$ the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory $\left(\chi \mathrm{PT}\right)$ to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral logarithmic parameter $\delta$ together with other low-energy parameters. Only for $m_{\pi }<~300\mathrm{MeV}$ do we obtain a consistent and stable fit with a constant $\delta$ which we determine to be 0.24(3)(4) (at the chiral scale ${\Lambda }_{\chi }=0.8\mathrm{}\mathrm{GeV}).\mathrm{}$ By comparing to the ${12}^3\times 28$ lattice, we estimate the finite volume effect to be about 2.7% for the smallest pion mass. We also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to $m_{\pi }\sim 500–600\mathrm{MeV}.$ The scale independent $\delta$ is determined to be 0.20(3) in this case. We study the quenched non-analytic terms in the nucleon mass and find that the coefficient $C_{1/2}$ in the nucleon mass is consistent with the prediction of one-loop $\chi \mathrm{PT}.$ We also obtain the low energy constant $L_5$ from $f_{\pi }.$ We conclude from this study that it is imperative to cover only the range of data with the pion mass less than $\sim 300\mathrm{MeV}$ in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop $\chi \mathrm{PT}.$

The analysis of certain singularities in scalar-tensor gravity contained in a recent paper is completed, and situations are pointed out in which these singularities cannot occur.

We extend the investigation of nonextremal enhançons, finding the most general solutions with the correct symmetry and charges. There are two families of solutions. One of these contains a solution with a regular horizon found previously; this previous example is shown to be the unique solution with a regular horizon. The other family generalizes a previous nonextreme extension of the enhançon, producing solutions with shells that satisfy the weak energy condition. We argue that identifying a unique solution with a shell requires input beyond supergravity.

The one-loop renormalization in field theories can be formulated in terms of the heat kernel expansion. In this paper we calculate leading contributions of discontinuities of background fields and their derivatives to the heat kernel coefficients. These results are then used to estimate contributions of the discontinuities to the Casimir energy. Sign of such contribution is defined solely by the order of discontinuous derivative. We also discuss renormalization in the presence of singular (delta-function) potentials. We show that an independent surface tension counterterm is necessary. This observation seems to resolve some contradictions in previous calculations.

A dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential is derived which sheds light on the determinant’s dependence on these quantities. This is done via a partial zeta regularization, formally applying a general formula for the zeta determinant of a differential operator in one variable with operator-valued coefficients. The resulting expression generalizes the known one for the free fermion determinant, obtained via Matsubara frequency summation, to the case of a general background gauge field; moreover there is no undetermined overall factor. Rigorous versions of the result are obtained in a continuous time–lattice space setting. The determinant expression reduces to a remarkably simple form in the low temperature limit. A program for using this to obtain insight into the QCD phase transition at zero temperature and nonzero density is outlined.

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for $N_f=2\mathrm{}$ and with exact numerical results obtained in the large-$N_f$ limit.

The Bousso bound requires that one-quarter of the area of a closed codimension-2 spacelike surface exceeds the entropy flux across a certain lightsheet terminating on the surface. The bound can be violated by quantum effects such as Hawking radiation. It is proposed that at the quantum level the bound be modified by adding to the area the quantum entanglement entropy across the surface. The validity of this quantum Bousso bound is proven in a two-dimensional large N dilaton gravity theory.

We have studied traversable Lorentzian wormholes by adding some matter source involving a dilaton field into the three-dimensional low-energy string theory. Through this experiment, it was shown that there were two types of wormhole solutions—the BTZ and black string wormholes—depending on the dilaton backgrounds, respectively. We are finally able to obtain desirable solutions that confine exotic matter near the throat of a wormhole by adjusting the NS charge.

In this article we will analyze the possibility of a nontrivial central extension of the Poisson algebra of the diffeomorphism generators which respect certain boundary conditions on the black hole bifurcation. The origin of a possible central extension in the algebra is due to the existence of boundary terms in the canonical generators, which are necessary to make them differentiable. The existence of such boundary terms depends on the exact boundary conditions that one takes. We will check two possible boundary conditions on the black hole bifurcation: fixed metric and fixed surface gravity. In the case of a fixed metric of the bifurcation the action acquires a boundary term but this term is canceled in the Legendre transformation and is thus absent in the Hamiltonian, and so in this case the possibility of a central extension is ruled out. In the case of fixed surface gravity the boundary term in the action is absent but therefore present in the Hamiltonian. Also in this case we will see that there is no central extension, also if there exist boundary terms in the generators.

By calculating the Newman-Penrose Weyl tensor components of a perturbed spherically symmetric space-time with respect to invariantly defined classes of null tetrads, we give a physical interpretation, in terms of gravitational radiation, of odd parity gauge invariant metric perturbations. We point out how these gauge invariants may be used in setting boundary and/or initial conditions in perturbation theory.