We determine the location ${\lambda }_c$ of the mobility edge in the spectrum of the hermitian Wilson operator on quenched ensembles. We confirm a theoretical picture of localization proposed for the Aoki phase diagram. When ${\lambda }_c>0$ we also determine some key properties of the localized eigenmodes with eigenvalues $|\lambda |<{\lambda }_c$. Our results lead to simple tests for the validity of simulations with overlap and domain-wall fermions.

The local Lorentz gauge represents a natural coordinate frame for an observer to analyze the effect of gravitational waves on detectors, and has been widely used to describe the response of resonant bars. Its application to laser interferometers has thus far been restricted to the long-wavelength regime, in which the separation between the test masses is much less than the wavelength of the gravitational waves. In this paper we show that the local Lorentz gauge can be used for calculations of geodesic deviations of the masses even when their separation is comparable to or greater than the wavelength of the gravitational waves. We find that a complete description of the gravitational waves in this gauge requires taking into account three different effects: displacements of the test masses, the gravitational redshift of light propagating between the masses, and variations in the rates of stationary clocks, all of which are induced by the gravitational wave. Only when taken together do these three effects represent a quantity which is translationally invariant and which can be observed in experiments. This translationally invariant quantity is identical to the response function calculated in the transverse traceless gauge.

We find numerical solutions of Einstein equations and scalar field equation for a global defect in higher dimensional spacetimes ($\ge 6$). We examine in detail the relation between the expansion rate $H$ and the symmetry-breaking scale $\eta$ and the number of extra dimension $n$ for these solutions. We find that even if the extra dimensions do not have a cigar geometry, the expansion rate $H$ grows as $\eta$ increases, which is opposite to what is needed for the recently proposed mechanism for solving the cosmological constant problem. We also find that the expansion rate $H$ decreases as $n$ increases.

The results of a search for point sources of high energy neutrinos in the northern hemisphere using data collected by AMANDA-II in the years 2000, 2001, and 2002 are presented. In particular, a comparison with the single-year result previously published shows that the sensitivity was improved by a factor of 2.2. The muon neutrino flux upper limits on selected candidate sources, corresponding to an $E_{\nu }^{-2}$ neutrino energy spectrum, are included. Sky grids were used to search for possible excesses above the background of cosmic ray induced atmospheric neutrinos. This search reveals no statistically significant excess for the three years considered.

We study exclusive radiative decays of the ${\rm Y}$ using soft-collinear effective theory and nonrelativistic QCD. In contrast to inclusive radiative decays at the endpoint we find that color-octet contributions are power suppressed in exclusive decays, and can safely be neglected, greatly simplifying the analysis. We determine the complete set of Lorentz structures that can appear in the SCET Wilson coefficients and match onto them using results from a previous calculation. We run these coefficients from the scale $M_{{\rm Y}}$ to the scale $\Lambda \sim 1\mathrm{G}\mathrm{e}\mathrm{V}$, thereby summing large logarithms. Finally we use our results to predict the ratio of branching fractions $B({\rm Y}\to \gamma f_2)/B(J/\psi \to \gamma f_2)$, $B(J/\psi \to \gamma f_2)/B({\psi }^{\prime }\to \gamma f_2)$, and the partial rate for ${\rm Y}\to \gamma \pi \pi$.

The theoretical predictions are given for the forward limit of the unpolarized spin-flip isovector generalized parton distribution function $(E^u-E^d)(x,\xi ,t)$ within the framework of the chiral quark soliton model, with full inclusion of the polarization of Dirac sea quarks. We observe that $[(H^u-H^d)+(E^u-E^d)](x,0,0)$ has a sharp peak around $x=0$, which we interpret as a signal of the importance of the pionic $q\overline{q}$ excitation with large spatial extension in the transverse direction. Another interesting indication given by the predicted distribution in combination with Ji’s angular momentum sum rule is that the $\overline{d}$ quark carries more angular momentum than the $\overline{u}$ quark in the proton, which may have some relation with the physics of the violation of the Gottfried sum rule.

Measurements by the Belle Collaboration of the exclusive production of two charmonia in $e^{+}{e}^{-}$ annihilation differ substantially from theoretical predictions. Till now, no conclusive explanation for this remarkable discrepancy has been provided. Even the origin of the discrepancy is not identified, yet. We suggest that the measurement of four-charm events in Belle data must provide a strong constraint in identifying the origin of this large discrepancy. Our prediction of the cross section for $e^{+}{e}^{-}\to c\overline{c}c\overline{c}$, in lowest order in strong coupling constant, at $\sqrt{s}=10.6\mathrm{GeV}$ is about $0.1\mathrm{pb}$. If measured four-charm cross section is compatible with the prediction based on perturbative QCD, it is very likely that factorization of the hadronization process from perturbative part may be significantly violated or there exists a new production mechanism. If the cross section for the four-charm event is also larger than the prediction like that for the exclusive $J/\psi +{\eta }_c$ production, perturbative QCD expansion itself will be proved to be unreliable and loses predictive power.

The muon decay parameter $\delta$ has been measured by the TWIST collaboration. We find $\delta =0.74964\pm 0.00066(\mathrm{\text{stat}}.)\pm 0.00112(\mathrm{\text{syst}}.)$, consistent with the standard model value of $3/4$. This result implies that the product $P_{\mu }\xi$ of the muon polarization in pion decay, $P_{\mu }$, and the muon decay parameter $\xi$ falls within the 90% confidence interval $0.9960<P_{\mu }\xi \le \xi <1.0040$. It also has implications for left-right-symmetric and other extensions of the standard model.

We find that a gauged matrix model of rectangular fermionic matrices (a matrix version of the fermion harmonic oscillator) realizes a quantum hall droplet with manifest particle-hole symmetry. The droplet consists of free fermions on the topology of a sphere. It is also possible to deform the Hamiltonian by double trace operators, and we argue that this device can produce two body potentials which might lead the system to realize a fractional quantum hall state on the sphere. We also argue that a single gauged fermionic quantum mechanics of Hermitian matrices realizes a droplet with an edge that has $c=1/2\mathrm{CFT}$ on it.

I investigate a new idea of perturbation theory in covariant canonical quantization. I present preliminary results for a toy model of a harmonic oscillator with a quartic perturbation, and show that this method reproduces the quantized spectrum of standard quantum theory. This result indicates that when the exact solutions to classical equations are not known, covariant canonical quantization via perturbation theory could be a viable approximation scheme for finding observables, and suggests a physically interesting way of extending the scope of covariant canonical quantization in quantum gravity

One of the principal goals of modern cosmology is to constrain the properties of dark energy. At present, numerous surveys are aiming to determine the equation of state, which is assumed constant due to our poor understanding of its behavior (and since higher order parametrizations lead to unwieldy errors). This raises the question—how does our “best-fit” equation of state relate to the true function, which may vary with redshift. Saini et al. [Mon. Not. R. Astron. Soc. 343, 533 (2003).] have demonstrated that the value of $w$ attained by a supernova study is well described by a weighted integral over the true function. Adopting a similar approach, we calculate the corresponding “weight function” for a fiducial cosmic shear survey. We disentangle contributions from the angular diameter distance and the growth factor, finding that they partially cancel each other out. Consequentially, the sensitivity to $w$ at high redshift is enhanced beyond that of supernova studies, and is comparable, if not higher, than lensing of the cosmic microwave background. This illustrates the complementary nature of the different techniques. Furthermore, we find that results which would naïvely be interpreted as inconsistent could arise from a time-dependent equation of state.

With (nonbarotropic) equations of state valid even when the neutron, proton, and electron content of neutron star cores is not in beta equilibrium, we study inertial and composition gravity modes of relativistic rotating neutron stars. We solve the relativistic Euler equations in the time domain with a three dimensional numerical code based on spectral methods, in the slow rotation, relativistic Cowling and anelastic approximations. Principally, after a short description of the gravity modes due to smooth composition gradients, we focus our analysis on the question of how the inertial modes are affected by nonbarotropicity of the nuclear matter. In our study, the deviation with respect to barotropicity results from the frozen composition of nonsuperfluid matter composed of neutrons, protons, and electrons, when beta equilibrium is broken by millisecond oscillations. We show that already for moderately fast rotating stars the increasing coupling between polar and axial modes makes those two cases less different than for very slowly rotating stars. In addition, as we directly solve the Euler equations, without coupling only a few number of spherical harmonics, we always find, for the models that we use, a discrete spectrum for the $l=m=2$ inertial mode. Finally, we conclude that, for nonbarotropic stars, the frequency of this mode, which is our main focus, decreases in a non-negligible way, whereas the time dependence of the energy transfer between polar and axial modes is substantially different due to the existence of low-frequencies gravity modes.

Using the CLEO II.V detector observing $e^{+}{e}^{-}$ collisions at around 10.6 GeV we search for neutral $D$ mixing in semileptonic $D^0$ decays tagged in charged $D^{*}$ decays. Combining the results from the $Ke\nu$ and $K^{*}e\nu$ channels we find that the rate for $D$ mixing is less than 0.0078 at $90\%$ C.L.

We study the properties of pions in twisted mass lattice QCD (with two degenerate flavors) using chiral perturbation theory ($\chi \mathrm{PT}$). We work to next-to-leading order (NLO) in a power-counting scheme in which $m_q\sim a{\Lambda }_{\mathrm{QCD}}^2$, with $m_q$ the physical quark mass and $a$ the lattice spacing. We argue that automatic $O(a)$ improvement of physical quantities at maximal twist, which has been demonstrated in general if $m_q\gg a{\Lambda }_{\mathrm{QCD}}^2$, holds even if $m_q\sim a{\Lambda }_{\mathrm{QCD}}^2$, as long as one uses an appropriate nonperturbative definition of the twist angle, with the caveat that we have shown this only through NLO in our chiral expansion. We demonstrate this with explicit calculations, for arbitrary twist angle, of all pionic quantities that involve no more than a single pion in the initial and final states: masses, decay constants, form factors, and condensates, as well as the differences between alternate definitions of twist angle. We also calculate the axial and pseudoscalar form factors of the pion, quantities which violate flavor and parity, and which vanish in the continuum limit. These are of interest because they are not automatically $O(a)$ improved at maximal twist. They allow a determination of the unknown low-energy constants introduced by discretization errors, and provide tests of the accuracy of $\chi \mathrm{PT}$ at NLO. We extend our results into the regime where $m_q\sim a^2{\Lambda }_{\mathrm{QCD}}^3$, and argue in favor of a recent proposal that automatic $O(a)$ improvement at maximal twist remains valid in this regime.

In this note we reply to the criticism by Corichi concerning our proposal for an equidistant area spectrum in loop quantum gravity. We further comment on the emission properties of black holes and on the statistics of links.

We study a $1/4$ Bogomol’nyi-Prasad-Sommerfield equation containing configurations made of walls, vortices, and monopoles in the Higgs phase, using the supersymmetric $U(N_{\mathrm{C}})$ gauge theories with eight supercharges with $N_{\mathrm{F}}$ fundamental hypermultiplets. We find the total moduli space to be the quotient of the space of holomorphic maps from the complex plane to the $N_{\mathrm{C}}\times N_{\mathrm{F}}$ matrix divided by the space of the holomorphic maps to $GL(N_{\mathrm{C}},\mathbf{C})$. We obtain all possible solutions exactly in the strong coupling limit where the moduli space reduces to the space of all holomorphic maps from a complex plane to the wall moduli space found recently, the deformed complex Grassmann manifold. Monopoles in the Higgs phase are also found in $U(1)$ gauge theory.

In spite of the growing observational evidence for dark matter and dark energy in the universe, their physical nature is largely unknown. In fact, several authors have proposed modifications of Newton’s law of gravity at cosmological scales to account for the apparent acceleration of the cosmic expansion. Inspired by such suggestions, we attempt to constrain possible deviations from Newtonian gravity by means of the clustering of SDSS (Sloan Digital Sky Survey) galaxies. To be specific, we assume a simple modification of Newton’s law with an additional Yukawa-type term characterized by the amplitude $\alpha$ and the length scale $\lambda$. Adopting spatially-flat universes dominated by cold dark matter and/or dark energy, we solve a linear perturbation equation for the growth of density fluctuations. In particular, we find an exact analytic solution for the Einstein-de Sitter case. Following the Peacock-Dodds prescription, we compute the nonlinear power spectra of mass fluctuations, perform a statistical comparison with the SDSS galaxy data, and derive constraints in the $\alpha$-$\lambda$ plane; for instance, we obtain the constraints of $-0.5<\alpha <0.6$ and $-0.8<\alpha <0.9$ ($99.7\%$ confidence level) for $\lambda =5h^{-1}$ Mpc and $10h^{-1}$ Mpc, respectively. We also discuss several future possibilities for improving our analysis.