The Hamiltonian reduction of $\mathrm{SU}\left(2\right)\mathrm{}$ Yang-Mills theory for an arbitrary $\theta$ angle to an unconstrained nonlocal theory of a self-interacting positive definite symmetric $3\times 3$ matrix field $S\left(x\right)\mathrm{}$ is performed. It is shown that, after exact projection to a reduced phase space, the density of the Pontryagin index remains a pure divergence, proving the $\theta$ independence of the unconstrained theory obtained. An expansion of the nonlocal kinetic part of the Hamiltonian in powers of the inverse coupling constant and truncation to lowest order, however, lead to violation of the $\theta$ independence of the theory. In order to maintain this property on the level of the local approximate theory, a modified expansion in the inverse coupling constant is suggested, which for a vanishing $\theta$ angle coincides with the original expansion. The corresponding approximate Lagrangian up to second order in derivatives is obtained, and the explicit form of the unconstrained analogue of the Chern-Simons current linear in derivatives is given. Finally, for the case of degenerate field configurations $S\left(x\right)\mathrm{}$ with $\mathrm{rank}\Vert S\Vert =1,$ a nonlinear σ-type model is obtained, with the Pontryagin topological term reducing to the Hopf invariant of the mapping from the three-sphere $S^3$ to the unit two-sphere $S^2$ in the Whitehead form.

We study counterterms of one- and two-point Green’s functions of some special operators in $\mathcal{N}=1\mathrm{}$ super Yang-Mills (SYM) theory from their supergravity (SUGRA) duals from the consideration of AdS conformal field theory or gauge-gravity correspondence. We consider both the Maldacena-Nunez solution and the Klebanov-Strassler-Tseytlin solution which are proposed as SUGRA duals of $\mathcal{N}=1\mathrm{}$ SYM theory. We obtain a radius/energy relation for each solution by comparing the SUGRA calculations with the field theory results. Using these relations we evaluate the $\beta$ function of $\mathcal{N}=1\mathrm{}$ SYM theory. We find that the leading order term can be accurately obtained for both solutions and the higher order terms exhibit some ambiguities. We discuss the origin of these ambiguities and conclude that more studies are needed to check whether these SUGRA solutions are exactly dual to $\mathcal{N}=1\mathrm{}$ SYM theory.

We investigate D-dimensional Lorentzian spacetimes in which all of the scalar invariants constructed from the Riemann tensor and its covariant derivatives are zero. These spacetimes are higher-dimensional generalizations of D-dimensional pp-wave spacetimes, which have been of interest recently in the context of string theory in curved backgrounds in higher dimensions.

The production of black holes in extra-dimensional brane-world theories can lead to detectable signals via the Hawking evaporation of the black hole to brane-localized standard model modes. We calculate, as a function of partial wave number and number of toroidally compactified extra dimensions, the leading correction to the energy spectrum of such Hawking radiation (the greybody factors) for decay into spin-1/2 fermions and spin-1 gauge fields localized on the standard model brane. We derive the associated improved differential emission rates for both types of fields. We provide both simple expressions for the leading behavior of the greybody factors in the low-energy limit $\omega r_H\ll 1$ and numerical evaluation of our full analytic expressions for the emission rates, valid for $\omega r_H\sim 1.$ The full analytic expressions demonstrate that both the greybody factors and emission rates are enhanced as the number of extra dimensions increases.

We study master variables in the Regge-Wheeler-Zerilli formalism. We show that a specific choice of new variables is suitable for studying perturbation theory from the viewpoint of radiation reaction calculations. With explicit definition of the improved master variables in terms of components of metric perturbations, we present the master equations, with source terms, and metric reconstruction formulas. In the scheme using these new variables, we do not need any time and radial integrations except for solving the master equation. We also show that the master variable for even parity modes which satisfies the same homogeneous equation as the odd-parity case, obtained via Chandrasekhar transformation, does not have the good property in this sense.

The metric perturbation induced by a particle in the Schwarzschild background is usually calculated in the Regge-Wheeler (RW) gauge, whereas the gravitational self-force is known to be given by the tail part of the metric perturbation in the harmonic gauge. Thus, to identify the gravitational self-force correctly in a specified gauge, it is necessary to find out a gauge transformation that connects these two gauges. This is called the gauge problem. As a direct approach to solve the gauge problem, we formulate a method to calculate the metric perturbation in the harmonic gauge on the Schwarzschild background. We apply the Fourier-harmonic expansion to the metric perturbation and reduce the problem to the gauge transformation of the Fourier-harmonic coefficients (radial functions) from the RW gauge to the harmonic gauge. We derive a set of decoupled radial equations for the gauge transformation. These equations are found to have a simple second-order form for the odd parity part and the forms of spin $s=0\mathrm{}$ and 1 Teukolsky equations for the even parity part. As a by-product, we correct typographical errors in Zerilli’s paper and present a set of corrected equations in Appendix A.

The effect of including a Gauss-Bonnet contribution in the bulk action is investigated within the context of the steep inflationary scenario. When inflation is driven by an exponential inflaton field, this Gauss-Bonnet term allows the spectral index of the scalar perturbation spectrum to take values in the range 0.944 and 0.989, thereby bringing the scenario in closer agreement with the most recent observations. Once the perturbation spectrum is normalized to the microwave background temperature anisotropies, the value of the spectral index is determined by the Gauss-Bonnet coupling parameter and the tension of the brane and is independent of the logarithmic slope of the potential.

In spherically symmetric, static spacetime, we show that only $j=1/2\mathrm{}$ fermions can satisfy both Einstein’s field equation and Dirac’s equation. It is also shown that neutrinos are able to have effective masses and cluster in the galactic halo when they are coupled to a global monopole situated at the galactic core. The astronomical implications of the results are discussed.

Spherically symmetric black holes produce, by strong field lensing, two infinite series of relativistic images, formed by light rays winding around the black hole at distances comparable to the gravitational radius. In this paper we address the relevance of the black hole spin for the strong field lensing phenomenology, focusing on trajectories close to the equatorial plane for simplicity. In this approximation, we derive a two-dimensional lens equation and formulas for the position and the magnification of the relativistic images in the strong field limit. The most outstanding effect is the generation of a nontrivial caustic structure. Caustics drift away from the optical axis and acquire finite extension. For a high enough black hole spin, depending on the source extension, we can practically observe only one image rather than two infinite series of relativistic images. In this regime, additional nonequatorial images may play an important role in the phenomenology.

The sky distribution of cosmic rays with energies above the “GZK cutoff” holds important clues to their origin. The AGASA data, although consistent with isotropy overall, shows evidence for small-angle clustering, and it has been argued that such clusters are aligned with BL Lacertae objects, implicating these as the sources. It has also been suggested that such clusters can arise if the cosmic rays come from the decays of very massive relic particles in the galactic halo, due to the expected clumping of cold dark matter. We examine these claims and show that both are, in fact, unjustified.

We study the sensitivity limits of a broadband gravitational-wave detector based on dual resonators such as nested spheres. We determine both the thermal and back-action noises when the resonators’ displacements are read out with an optomechanical sensor. We analyze the contributions of all mechanical modes, using a new method to deal with the force-displacement transfer functions in the intermediate frequency domain between the two gravitational-wave sensitive modes associated with each resonator. This method gives an accurate estimate of the mechanical response, together with an evaluation of the estimate error. We show that very high sensitivities can be reached on a wide frequency band for realistic parameters in the case of a dual-sphere detector.

We propose an extension to the recently proposed extranatural or gauge inflation scenario in which the radius modulus field around which the Wilson loop is wrapped assists inflation as it shrinks. We discuss how this might lead to more generic initial conditions for inflation.

We discuss the importance of including baryons in analyses of unified dark matter scenarios, focusing on toy models involving a generalized Chaplygin gas. We determine observational constraints on this unified dark matter scenario coming from large-scale structure, type Ia supernovae and CMB data showing how this component can bring about a different behavior from the classical cold dark matter model with a cosmological constant and thus motivate further studies of this type of models. We also speculate on interesting new features which are likely to be important on nonlinear scales in this context.

We estimate the Coulomb energy of static quarks from a Monte Carlo calculation of the correlator of timelike link variables in the Coulomb gauge. We find, in agreement with Cucchieri and Zwanziger, that this energy grows linearly with distance at large quark separations. The corresponding string tension, however, is several times greater than the accepted asymptotic string tension, indicating that a state containing only static sources, with no constituent gluons, is not the lowest energy flux tube state. The Coulomb energy is also measured on thermalized lattices with center vortices removed by the de Forcrand–D’Elia procedure. We find that when vortices are removed, the Coulomb string tension vanishes.

We evaluate the renormalization factors of the domain-wall fermion system with various improved gauge actions at the one-loop level. The renormalization factors are calculated for the quark wave function, quark mass, bilinear quark operators, and three- and four-quark operators in the modified minimal subtraction $\left(\overline{\mathrm{MS}}\right)$ scheme with dimensional reduction as well as with the naive dimensional regularization. We also present detailed results in mean field improved perturbation theory.

The soft mode near the critical end point in the phase diagram of the two-flavor Nambu–Jona-Lasinio model is investigated within the leading ${1/N}_c$ approximation, with $N_c$ being the number of colors. It is explicitly shown by studying the spectral function of the scalar channel that the relevant soft mode is the scalar density fluctuation, which is coupled with the quark number density, while the sigma meson mode stays massive.

The recent observation of the decay $B^0\to {\Lambda }_c^{+}\overline{p}$ suggests that related decays may soon be visible at $e^{+}{e}^{-}$ colliders. It is shown how these decays can shed light on strong final-state phases and amplitudes involving the spectator quark, both of which are normally expected to be small in B decays.

We apply a phenomenological approach based on nonlinear Regge trajectories to glueball states. The parameters, i.e., the intercept and threshold, or trajectory termination point beyond which no bound states should exist, are determined from Pomeron (scattering) data. The systematic errors inherent to the approach are discussed. We then predict the masses of the glueballs on the tensor trajectory. For comparison, the approach is applied to available quenched lattice data. We find a discrepancy between the lattice-based thresholds and the Pomeron threshold that we extract from data.

Higgs bosons with enhanced coupling to bottom quarks are copiously produced at hadron colliders via $b\overline{b}\to h,$ where the initial b quarks reside in the proton sea. We reexamine the calculation of the next-to-leading-order cross section for this process and argue that the appropriate factorization scale for the b distribution functions is approximately $m_h/4,$ rather than $m_h,$ as had been previously assumed. This greatly improves the convergence of the perturbation series, and yields a result with mild factorization-scale dependence. We also show that the leading-order calculation of $g\overrightarrow{g}b\overline{b}h,$ integrated over the momenta of the final-state particles, is very sensitive to the factorization and renormalization scales. For scales of order $m_h/4\mathrm{}$ the $g\overrightarrow{g}b\overline{b}h$ cross section is comparable to that of $b\overline{b}\to h,$ in contrast with the order-of-magnitude discrepancy between these two calculations for the scale $m_h.$ The result we obtain improves the prospects for Higgs-boson discovery at hadron colliders for large values of $\tan \beta .$

We find that the normal muon polarization in the decay $\overrightarrow{K}\mu {\nu }_{\mu }\gamma$ is very sensitive to the values of the kaon vector $F_V$ and axial-vector $F_A$ form factors. It is shown that the ongoing KEK-E246 experiment can definitely determine the signs of the sum of the form factors if their difference is fixed from other considerations. This method can also verify the form factor values and signs obtained from the $K^{+}\to l^{+}{\nu }_l{e}^{+}{e}^{-}$ decays. A new experiment with sensitivity to the normal and transverse muon polarizations of about ${10}^{-4}$ will provide a unique possibility to determine the $F_V$ and $F_A$ values with a few percent accuracy.