The calculation of the $I=2\mathrm{}$ pion scattering length in quenched lattice QCD is reexamined. The calculation is carried out with the Wilson fermion action employing Lüscher’s finite size scaling method at $\beta =5.9,$ $6.1,$ and $6.3$ corresponding to the range of lattice spacing $a\simeq 0.12-0.07\mathrm{fm}.$ We obtain in the continuum limit $a_0{/m}_{\pi }=-2.09\left(35\right)\mathrm{}1/{\mathrm{GeV}}^2,$ which is consistent with the prediction of chiral perturbation theory $a_0{/m}_{\pi }=-2.265\left(51\right)1/{\mathrm{GeV}}^2.$

The equation of state of Hamiltonian lattice QCD at finite density is examined in the strong coupling limit by constructing a solution to the equation of motion corresponding to an effective Hamiltonian describing the ground state of the many body system. This solution exactly diagonalizes the Hamiltonian to second order in field operators for all densities and is used to evaluate the vacuum energy density from which we obtain the equation of state. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanical instability. Our result is in qualitative agreement with continuum models and should be verifiable by future lattice simulations of strongly coupled QCD at finite density.

We present an approximate next-to-next-to-leading-order evaluation of the QCD form factor resumming large logarithmic perturbative contributions in semi-inclusive heavy flavor decays.

The weak radiative Cabibbo allowed decays $D^{+}\to K^0{\pi }^{+}\gamma$ and $D^0\to K^{-}{\pi }^{+}\gamma$ with nonresonant $K\pi$ are investigated by relying on the factorization approximation for the nonleptonic weak transitions and the model which combines the heavy quark effective theory and the chiral Lagrangian approach. The dominant contributions to the amplitudes come from the long-distance effects. The decay amplitude has both parity violating and parity conserving parts. The parity violating part also includes a bremsstrahlung contribution. The branching ratio obtained for the parity conserving part is of the order ${10}^{-4}$ for the $D^0\to K^{-}{\pi }^{+}\gamma$ decay and ${10}^{-5}$ for $D^{+}\to K^0{\pi }^{+}\gamma ,$ when the effect of light vector mesons is included, and smaller otherwise. The branching ratio for the parity violating part with a photon energy cut of $50\mathrm{MeV}$ is close to ${10}^{-3}$ for the $D^0$ decay and $4\times {10}^{-4}$ for the $D^{+}$ decay. We present Dalitz plots and energy spectra for both transitions as derived from our model and we probe the role of the light vector mesons in these decays.

We present a new chiral quark model for mesons involving a heavy and a light (anti) quark. The model relates various combinations of a quark-meson coupling constant and loop integrals to physical quantities. Then, some quantities may be predicted and some used as input. The extension from other similar models is that the present model includes the lowest order gluon condensate of the order $(300\mathrm{}\mathrm{MeV}{)}^4$ determined by the mass splitting of the $0^{-}$ and the $1^{-}$ heavy meson states. Within the model, we find a reasonable description of parameters such as the decay constants $f_B$ and $f_D,$ the Isgur-Wise function and the axial vector coupling $g_A$ in chiral perturbation theory for light and heavy mesons.

Realization of the conformal higher spin symmetry on the 4D massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized $\mathcal{N}=4\mathrm{}$ super Yang-Mills theory, are considered in some detail. Duality between nonunitary field-theoretical representations and the unitary doubleton-type representations of the 4D conformal algebra $\mathrm{su}(2,2)\mathrm{}$ is formulated in terms of a Bogolyubov transform. The set of 4D massless fields of all spins is shown to form a representation of $\mathrm{sp}\left(8\right).$ The results obtained are extended to the generalized superspace invariant under $\mathrm{osp}(L,2M)\mathrm{}$ supersymmetries. A world line particle interpretation of the free higher spin theories in the $osp(2\mathrm{}\mathcal{N},2M)$ invariant (super)space is given. Compatible with unitarity, free equations of motion in the $\mathrm{osp}(L,2M)\mathrm{}$ invariant (super)space are formulated. A conjecture about the chain of ${\mathrm{AdS}}_{d+1\mathrm{}}/{\mathrm{CFT}}_d\to {\mathrm{AdS}}_d/{\mathrm{CFT}}_{d-1}\to \cdot \cdot \cdot$ (where CFT indicates conformal field theory) dualities in the higher spin gauge theories is proposed.

We present a new scenario for baryogenesis in the context of heterotic brane-world models. The baryon asymmetry of the universe is generated at a small-instanton phase transition which is initiated by a moving brane colliding with the observable boundary. We demonstrate, in the context of a simple model, that reasonable values for the baryon asymmetry can be obtained. As a byproduct we find a new class of moving-brane cosmological solutions in the presence of a perfect fluid.

Cubic kilometer neutrino telescopes are capable of probing fundamental questions of ultrahigh energy neutrino interactions. There is currently great interest in neutrino interactions caused by low-scale, extra dimension models. Above 1 PeV the cross section in low scale gravity models rises well above the total standard model cross section. We assess the observability of this effect in the 1–1000 PeV energy range of kilometer-scale detectors, emphasizing several new points that hinge on the enhancement of neutral current cross sections with respect to charged current cross sections. A major point is the importance of “feed-down” regeneration of upward neutrino flux, driven by new-physics neutral current interactions in the flux evolution equations. Feed-down is far from negligible, and it is essential to include its effect. We then find that the angular distribution of events has high discriminating value in separating models. In particular the “up-to-down” ratio between upward- and downward-moving neutrino fluxes is a practical diagnostic tool which can discriminate between models in the near future. The slope of the angular distribution, in the region of maximum detected flux, is also substantially different in low-scale gravity and the standard model. These observables are only weakly dependent on astrophysical flux uncertainties. We conclude that angular distributions can reveal a breakdown of the standard model and probe the new physics beyond, as soon as data become available.

We study the IR-UV connection in noncommutative ${\phi }^3$ theory as well as in noncommutative QED from the point of view of the dispersion relation for self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of noncommutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed.

We present new non-Abelian solitonic configurations in the low energy effective theory describing a collection of N parallel D1-branes. These configurations preserve $1/4,1/8,1/16$ and $1/32$ of the spacetime supersymmetry. They are solutions to a set of generalized Nahm equations which are related to self-duality equations in eight dimensions. Our solutions represent D1-branes which expand into fuzzy funnel configurations ending on collections of intersecting D3-branes. Supersymmetry dictates that such intersecting D3-branes must lie on a calibrated three-surface of spacetime and we argue that the generalized Nahm equations encode the data for the construction of magnetic monopoles on the relevant three-surfaces.

We study the multiplicity of BPS domain walls in $\mathcal{N}=1\mathrm{}$ super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced world volume theory, which is invariant under the deformation to the Higgs phase. The world volume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped $D4\mathrm{}$-branes in type IIA string theory.

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-Abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher dimensional, spacetime being kept always four dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast with the ordinary Kaluza-Klein models, this theory defines a natural length scale for the compact submanifold of the fiber space, which is shown to be of the order of the Planck length.

We review the detectability of gravitational waves generated by oscillations excited during a phase transition from hadronic matter to deconfined quark-gluon matter in the core of a neutron star. Neutron star properties were computed using a Boguta-Bodmer based model and the MIT bag model. The maximum energy available to excite mechanical oscillations into the star is estimated by the energy difference between the configurations with and without a quark-gluon matter core. On basis of the planned sensitivity of present laser interferometers (VIRGO or LIGO I) and those of the next generation (LIGO II), the maximum volume to be probed by these experiments is determined. These results are used as an indication of the potential detectability of neutron stars as sources of gravitational waves. Our results indicate that the maximum distance probed by the detectors of the first generation is well beyond M31, whereas the second generation detectors will probably see phase transition events at distances two times longer, but certainly not yet attaining the Virgo cluster.

The initial data sets for the five-dimensional Einstein equation have been examined. The system is designed such that the black hole $\left(\simeq S^3\right)$ or the black ring $(\simeq S^2\times S^1)$ can be found. We have found that the typical length of the horizon can become arbitrarily large but the area of characteristic closed two-dimensional submanifold of the horizon is bounded above by the typical mass scale. We conjecture that the isoperimetric inequality for black holes in n-dimensional space is given by $V_{n-2}\lesssim GM,$ where $V_{n-2}$ denotes the volume of a typical closed (n-2)-section of the horizon and M is typical mass scale, rather than $C\lesssim {\mathrm{}\left(\mathrm{GM}\right)\mathrm{}}^{1/\left(n-2\right)}$ in terms of the hoop length C, which holds only when $n=3.\mathrm{}$

We claim that a composite fiber bundle satisfactorily serves as the geometrical structure underlying gauge theories of spacetime groups, such as the Poincaré gauge theory. A trivial extension of the approach to include internal symmetries also provides a unique mathematical scheme in which gravitation and the remaining forces are put together and treated in a common fiber bundle language. The result is a homogeneous characterization of interactions, gravity included, exclusively by means of connections.

We explore a classical instability of spacetimes of dimension $D>\mathrm{}4.\mathrm{}$ First, we consider static solutions: generalized black holes and brane world metrics. The dangerous mode is a tensor mode on an Einstein base manifold of dimension $D-2.$ A criterion for instability is found for the generalized Schwarzschild, AdS-Schwarzschild and topological black hole spacetimes in terms of the Lichnerowicz spectrum on the base manifold. Secondly, we consider perturbations in time-dependent solutions: Generalized dS and AdS. Thirdly we show that, subject to the usual limitations of a linear analysis, any Ricci flat spacetime may be stabilized by embedding into a higher dimensional spacetime with cosmological constant. We apply our results to pure AdS black strings. Finally, we study the stability of higher dimensional “bubbles of nothing.”

We present many-parameter families of strongly and symmetric hyperbolic formulations of Einstein’s equations that include quite general algebraic and live gauge conditions for the lapse. The first system that we present has $30$ variables and incorporates an algebraic relationship between the lapse and the determinant of the three metric that generalizes the densitized lapse prescription. The second system has $34$ variables and uses a family of live gauges that generalizes the Bona-Masso slicing conditions. These systems have free parameters even after imposing hyperbolicity and are expected to be useful in 3D numerical evolutions. We discuss under what conditions there are no superluminal characteristic speeds.

The dimensional reduction of black hole solutions in four-dimensional (4D) general relativity is performed and new 3D black hole solutions are obtained. Considering a 4D spacetime with one spacelike Killing vector, it is possible to split the Einstein-Hilbert-Maxwell action with a cosmological term in terms of 3D quantities. Definitions of quasilocal mass and charges in 3D spacetimes are reviewed. The analysis is then particularized to the toroidal charged rotating anti–de Sitter black hole. The reinterpretation of the fields and charges in terms of a three-dimensional point of view is given in each case, and the causal structure analyzed.

We consider the two-brane Randall-Sundrum (RS) model with bulk gauge fields. We carefully match the bulk theory to a 4D low-energy effective Lagrangian. In addition to the four-fermion operators induced by KK exchange we find that large negative S and T parameters are induced in the effective theory. This is a tree-level effect and is a consequence of the shapes of the W and Z wave functions in the bulk. Such effects are generic in extra dimensional theories where the standard model (SM) gauge bosons have nonuniform wave functions along the extra dimension. The corrections to precision electroweak observables in the RS model are mostly dominated by S. We fit the parameters of the RS model to the experimental data and find somewhat stronger bounds than previously obtained; however, the standard model bound on the Higgs boson mass from precision measurements can only be slightly relaxed in this theory.

We derive a condition for converging a common evolutionary track for k-essence (a scalar field dark energy with noncanonical kinetic terms). For the Lagrangian density $V\left(\phi \right)W\left(X\right)\mathrm{}$ with $X={\dot{\phi }}^2/2,$ we find that tracker solutions with $w_{\phi }<w_B$ exist if $\Gamma \equiv V^{″}{V/(V}^{\prime }{)}^2>3/2.\mathrm{}$ Here $w_{\phi }{(w}_B)$ is the equation of state of the scalar field (background radiation or matter). Our condition may be useful for examining the existence of attractorlike behavior in cosmology with k-essence (for example, a rolling tachyon).