Compact manifolds of $G_2$ holonomy may be constructed by dividing a seven-torus by some discrete symmetry group and then blowing up the singularities of the resulting orbifold. We classify possible group elements that may be used in this construction and use this classification to find a set of possible orbifold groups. We then derive the moduli Kähler potential for M-theory on the resulting class of $G_2$ manifolds with blown-up codimension four singularities.

In recent papers [D. N. Vollick, Phys. Rev. D 68, 063510 (2003)][D. N. Vollick, Classical Quantum Gravity 21, 3813 (2004).] I have argued that the observed cosmological acceleration can be accounted for by the inclusion of a $1/R$ term in the gravitational action in the Palatini formalism. Subsequently, Flanagan [Phys. Rev. Lett. 92, 071101 (2004)][Class. Quant. Grav. 21, 3817 (2004)] argued that this theory is equivalent to a scalar-tensor theory which produces corrections to the standard model that are ruled out experimentally. In this article I examine the Dirac field coupled to $1/R$ gravity. The Dirac action contains the connection which was taken to be the Christoffel symbol, not an independent quantity, in the papers by Flanagan. Since the metric and connection are taken to be independent in the Palatini approach it is natural to allow the connection that appears in the Dirac action to be an independent quantity. This is the approach that is taken in this paper. The resulting theory is very different and much more complicated than the one discussed in Flanagan’s papers.

We combine the measurements of luminosity dependence of bias with the luminosity dependent weak lensing analysis of dark matter around galaxies to derive the galaxy bias and constrain amplitude of mass fluctuations. We take advantage of theoretical and simulation predictions that predict that, while halo bias is rapidly increasing with mass for high masses, it is nearly constant in low mass halos. We use a new weak lensing analysis around the same Sloan Digital Sky Survey (SDSS) galaxies to determine their halo mass probability distribution. We use these halo mass probability distributions to predict the bias for each luminosity subsample. Galaxies below $L_{*}$ are antibiased with $b<1$ and for these galaxies bias is only weakly dependent on luminosity. In contrast, for galaxies above $L_{*}$ bias is rapidly increasing with luminosity. These observations are in an excellent agreement with theoretical predictions based on weak lensing halo mass determination combined with halo bias-mass relations. We find that for standard cosmological parameters theoretical predictions are able to explain the observed luminosity dependence of bias over six magnitudes in absolute luminosity. We combine the bias constraints with those from the Wilkinson Microwave Anisotropy Probe (WMAP) and the SDSS power spectrum analysis to derive new constraints on bias and ${\sigma }_8$. For the most general parameter space that includes running and neutrino mass, we find ${\sigma }_8=0.88\pm 0.06$ and $b_{*}=0.99\pm 0.07$. In the context of spatially flat models we improve the limit on the neutrino mass for the case of three degenerate families from $m_{\nu }<0.6\mathrm{e}\mathrm{V}$ without bias to $m_{\nu }<0.18\mathrm{e}\mathrm{V}$ with bias (95% C.L.), which is weakened to $m_{\nu }<0.24\mathrm{e}\mathrm{V}$ if running is allowed. The corresponding limit for $3\mathrm{\text{massless}}+1\mathrm{\text{massive}}$ neutrino is 1.37 eV.

The $2^n$ different n-point functions that occur in real-time thermal field theory are Fourier transformed to real energies. Because of branch cuts in various energy variables, none of these functions can be extended analytically to complex energies. The known linear combinations that form the fully retarded and advanced functions can be extended analytically. It is proven that no other linear combinations have an analytic extension to complex energies.

We discuss $B$-meson signatures of a Supersymmetric U(2) flavor model, with relatively light (electroweak scale masses) third generation right-handed scalars. We impose current $B$ and $K$ meson experimental constraints on such a theory, and obtain expectations for $B_d\to X_s\gamma$, $B_d\to X_{s}g$, $B_d\to X_s{\ell }^{+}{\ell }^{-}$, $B_d\to \varphi K_s$, $B_s{\overline{B}}_s$ mixing and the dilepton asymmetry in $B_s$. We show that such a theory is compatible with all current data, and furthermore, could reconcile the apparent deviations from Standard Model predictions that have been found in some experiments.

The decays of nonstrange negative parity baryons via the emission of single $\pi$ and $\eta$ mesons are analyzed in the framework of the $1/N_c$ expansion. A basis of spin-flavor operators for the partial wave amplitudes is established to order $1/N_c$ and the unknown effective coefficients are determined by fitting to the $S$- and $D$-wave partial widths as provided by the Particle Data Group. A set of relations between widths that result at the leading order, i.e., order $N_c^0$, is given and tested with the available data. The rather large errors of the input partial widths, that result from the often discrepant results for the resonance parameters from different analyses of the data, lead to a rather good fit at the leading order $N_c^0$. The next to leading order fit fails for the same reason to pin down with satisfactory accuracy the subleading effective coefficients. The hierarchy expected from the $1/N_c$ expansion is however reflected in the results.

We analyze, in the framework of AdS/CFT correspondence, the gauge theory phase structure that is supposed to be dual to the recently found nonsupersymmetric dilatonic deformations to $Ad{S}_5\times S^5$ in type IIB string theory. Analyzing the probe D7-brane dynamics in the backgrounds of our interest, which corresponds to the fundamental $\mathcal{N}=2$ hypermultiplet, we show that the chiral bi-fermion condensation responsible for spontaneous chiral symmetry breaking is not logically related to the phenomenon of confinement.

We consider a U(1) gauge field theory with fermion fields (or with scalar fields) that live in a space with $\delta$ extra compact dimensions, and we compute the fermion-induced quantum energy in the presence of a constant magnetic field, which is directed towards the $x_3$ axis. Our motivation is to study the effect of extra dimensions on the asymptotic behavior of the quantum energy in the strong field limit ($eB>>M^2$), where $M=1/R$. We see that the weak logarithmic growth of the quantum energy for four dimensions is modified by a rapid power growth in the case of the extra dimensions.

We present a weak-coupling Yang-Mills model supporting non-Abelian magnetic flux tubes and non-Abelian confined magnetic monopoles. In the dual description the magnetic flux tubes are prototypes of the QCD strings. Dualizing the confined magnetic monopoles we get gluelumps which convert a “QCD string” in the excited state to that in the ground state. Introducing a mass parameter $m$ we discover a phase transition between the Abelian and non-Abelian confinement at a critical value $m=m_{*}\sim \Lambda$. Underlying dynamics are governed by a $Z_N$ symmetry inherent to the model under consideration. At $m>m_{*}$ the $Z_N$ symmetry is spontaneously broken, resulting in $N$ degenerate $Z_N$ (Abelian) strings. At $m<m_{*}$ the $Z_N$ symmetry is restored, the degeneracy is lifted, and the strings become non-Abelian. We calculate tensions of the non-Abelian strings, as well as the decay rates of the metastable strings, at $N\gg 1$.

Higher-order theories of gravity have recently attracted a lot of interest as alternative candidates to explain the observed cosmic acceleration without the need of introducing any scalar field. A critical ingredient is the choice of the function $f(R)$ of the Ricci scalar curvature entering the gravity Lagrangian and determining the dynamics of the Universe. We describe an efficient procedure to reconstruct $f(R)$ from the Hubble parameter $H$ depending on the redshift $z$. Using the metric formulation of $f(R)$ theories, we derive a third order linear differential equation for $f[R(z)]$ which can be numerically solved after setting the boundary conditions on the basis of physical considerations. Since $H(z)$ can be reconstructed from the astrophysical data, the method we present makes it possible to determine, in principle, what is the $f(R)$ theory which best reproduces the observed cosmological dynamics. Moreover, the method allows to reconcile dark energy models with $f(R)$ theories finding out what is the expression of $f(R)$ which leads to the same $H(z)$ of the given quintessence model. As interesting examples, we consider “quiessence” (dark energy with constant equation of state) and the Chaplygin gas.

Lepton flavor violating Higgs boson decays are studied within the context of seesaw models with Majorana massive neutrinos. Two models are considered: the SM-seesaw, with the standard model particle content plus three right-handed neutrinos, and the MSSM-seesaw, with the minimal supersymmetric standard model particle content plus three right-handed neutrinos and their supersymmetric partners. The widths for these decays are derived from a full one-loop diagrammatic computation in both models, and they are analyzed numerically in terms of the seesaw parameters, namely, the Dirac and Majorana mass matrices. Several possible scenarios for these mass matrices that are compatible with neutrino data are considered. In the SM-seesaw case, very small branching ratios are found for all studied scenarios. These ratios are explained as a consequence of the decoupling behavior of the heavy right-handed neutrinos. In contrast, in the MSSM-seesaw case, sizable branching ratios are found for some of the leptonic flavor violating decays of the MSSM neutral Higgs bosons and for some choices of the seesaw matrices and MSSM parameters. The relevance of the two competing sources of lepton flavor changing interactions in the MSSM-seesaw case is also discussed. The nondecoupling behavior of the supersymmetric particles contributing in the loop diagrams is finally shown.

The contribution of the $a_1(1260)$ meson to the amplitudes of the decays $\rho (770)\to 4\pi$, $\omega (782)\to 5\pi$, and $\varphi (1020)\to 5\pi$ is analyzed in the chiral model of pseudoscalar, vector, and axial vector mesons based on the generalized hidden local symmetry added with the anomalous terms. The analysis shows that inclusion of $a_1$ meson in the intermediate states results in enhancement of the branching ratios of the above decays by the factor ranging from 1.3 to 1.9 depending on the mass of $a_1$ meson ranging from 1.23 GeV to $m_{a_1}=m_{\rho }\sqrt{2}=1.09\mathrm{G}\mathrm{e}\mathrm{V}$, the greater factor standing in case of lower mass of the $a_1$.

We have recently shown that dense quark matter possesses a color ferromagnetic phase in which a stable color-magnetic field arises spontaneously. This ferromagnetic state has been known to be Savvidy vacuum in the vacuum sector. Although the Savvidy vacuum is unstable, the state is stabilized in the quark matter. The stabilization is achieved by the formation of quantum Hall states of gluons, that is, by the condensation of the gluon's color charges transmitted from the quark matter. The phase is realized between the hadronic phase and the color superconducting phase. After a review of quantum Hall states of electrons in semiconductors, we discuss the properties of quantum Hall states of gluons in quark matter in detail. Especially, we evaluate the energy of the states as a function of the coupling constant. We also analyze solutions of vortex excitations in the states and evaluate their energies. We find that the states become unstable as the gauge coupling constant becomes large, or the chemical potential of the quarks becomes small, as expected. On the other hand, with the increase of the chemical potential, the color superconducting state arises instead of the ferromagnetic state. We show the region of the chemical potential of the quarks in which the color ferromagnetic phase is realized. We also show that the quark matter produced by heavy ion collisions generates observable strong magnetic field $\sim {10}^{14}\mathrm{G}$ when it is in the ferromagnetic phase.

We compute the order ${\alpha }_s^2$ corrections to the one particle inclusive electroproduction cross section of hadrons with nonvanishing transverse momentum. We perform the full calculation analytically, and obtain the expression of the factorized (finite) cross section at this order. We compare our results with H1 data on forward production of ${\pi }^0$, and discuss the phenomenological implications of the rather large higher order contributions obtained in that case. Specifically, we analyze the cross section sensitivity to the factorization and renormalization scales, and to the input fragmentation functions, over the kinematical region covered by data. We conclude that the data is well described by the $\mathcal{O}({\alpha }_s^2)$ predictions within the theoretical uncertainties and without the inclusion of any physics content beyond the Dokshitzer-Grivov-Lipatov-Altarelli-Parisi (DGLAP) approach.

We report improved measurements of the partial rate asymmetry (${\mathcal{A}}_{CP}$) in $B\to hh$ decays with $140{\mathrm{f}\mathrm{b}}^{-1}$ of data collected with the Belle detector at the KEKB $e^{+}{e}^{-}$ collider. Here $h$ stands for a charged or neutral pion or kaon and in total five decay modes are included: $K^{\mp }{\pi }^{\pm }$, $K_S^0{\pi }^{\mp }$, $K^{\mp }{\pi }^0$, ${\pi }^{\mp }{\pi }^0$, and $K_S^0{\pi }^0$. The flavor of the last decay mode is determined from the accompanying $B$ meson. Using a data sample 4.7 times larger than that of our previous measurement, we find ${\mathcal{A}}_{CP}(K^{\mp }{\pi }^{\pm })-0.088\pm 0.035\pm 0.013$, $2.4\sigma$ from zero. Results for other decay modes are also presented.

We describe searches for $B$ meson decays to the charmless vector-vector final states $\omega K^{*}$ and $\omega \rho$ in $89\times {10}^6$ $B\overline{B}$ pairs produced in $e^{+}{e}^{-}$ annihilation at $\sqrt{s}=10.58\mathrm{G}\mathrm{e}\mathrm{V}$. We measure the following branching fractions in units of ${10}^{-6}$: $\mathcal{B}(B^0\to \omega K^{*0})={3.4}_{-1.6}^{+1.8}\pm 0.4(<6.0)$, $\mathcal{B}(B^{+}\to \omega K^{*+})={3.5}_{-2.0}^{+2.5}\pm 0.7(<7.4)$, $\mathcal{B}(B^0\to \omega {\rho }^0)={0.6}_{-1.1}^{+1.3}\pm 0.4(<3.3)$, and $\mathcal{B}(B^{+}\to \omega {\rho }^{+})={12.6}_{-3.3}^{+3.7}\pm 1.6$. The first error quoted is statistical, the second systematic, and the upper limits are defined at 90% confidence level. For $B^{+}\to \omega {\rho }^{+}$ we also measure the longitudinal spin alignment fraction $f_L={0.88}_{-0.15}^{+0.12}\pm 0.03$ and charge asymmetry ${\mathcal{A}}_{\mathrm{c}\mathrm{h}}=(5\pm 26\pm 2)\%$.

We study the decays $B^{-}\to D^{*0}{\pi }^{-}$ and $B^{-}\to D^{*0}{K}^{-}$, where the $D^{*0}$ decays into $D^0{\pi }^0$, with the $D^0$ reconstructed in the $CP$-even ($CP+$) eigenstates $K^{-}{K}^{+}$ and ${\pi }^{-}{\pi }^{+}$ and in the (non-$CP$) channels $K^{-}{\pi }^{+}$, $K^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$, and $K^{-}{\pi }^{+}{\pi }^0$. Using a sample of about $123\times {10}^6$ $B\overline{B}$ pairs, we measure the ratios of decay rates $R_{\mathrm{n}\mathrm{o}\mathrm{n}-CP}^{*}\equiv \frac{\mathcal{B}(B^{-}\to D_{\mathrm{n}\mathrm{o}\mathrm{n}-CP}^{*0}{K}^{-})}{\mathcal{B}(B^{-}\to D_{\mathrm{n}\mathrm{o}\mathrm{n}-CP}^{*0}{\pi }^{-})}=0.0813\pm 0.0040{(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})}_{-0.0031}^{+0.0042}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}),$ and provide the first measurements of $R_{CP+}^{*}\equiv \frac{\mathcal{B}(B^{-}\to D_{CP+}^{*0}{K}^{-})}{\mathcal{B}(B^{-}\to D_{CP+}^{*0}{\pi }^{-})}=0.086\pm 0.021(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.007(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}),$ and of the $CP$ asymmetry $A_{CP+}^{*}\equiv \frac{\mathcal{B}(B^{-}\to D_{CP+}^{*0}{K}^{-})-\mathcal{B}(B^{+}\to D_{CP+}^{*0}{K}^{+})}{\mathcal{B}(B^{-}\to D_{CP+}^{*0}{K}^{-})+\mathcal{B}(B^{+}\to D_{CP+}^{*0}{K}^{+})}=-0.10\pm 0.23{(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})}_{-0.04}^{+0.03}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}).$

We revisit and complete the study of curved BPS-domain walls in matter-coupled $5D$, $\mathcal{N}=2$ supergravity and carefully analyze the relation to gravitational theories known as “fake supergravities.” We first show that curved BPS-domain walls require the presence of nontrivial hypermultiplet scalars, whereas walls that are solely supported by vector multiplet scalars are necessarily flat, due to the constraints from very special geometry. We then recover fake supergravity as the effective description of true supergravity where one restricts the attention to the flowing scalar field of a given BPS-domain wall. In general, however, true supergravity can be simulated by fake supergravity at most locally, based upon two choices: (i) a suitable adapted coordinate system on the scalar manifold, such that only one scalar field plays a dynamical role, and (ii) a gauge fixing of the SU(2) connection on the quaternionic-Kähler manifold, as this connection does not fit the simple formalism of fake supergravity. Employing these gauge and coordinate choices, the BPS-equations for both vector and hypermultiplet scalars become identical to the fake supergravity equations, once the line of flow is determined by the full supergravity equations.

Using twistor-space intuition, Cachazo, Svrček and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define non-MHV vertices, and show how to use them to give a recursive construction of these amplitudes. We also use them to illustrate the equivalence of various twistor-space prescriptions, and to determine the associated combinatoric factors.

Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which the exponent of the nonlinear term is either $p=5$ or $p=7$. Near the threshold of singularity formation, numerical solutions suggest an approach to self-similarity for the $p=7$ case and an approach to a scale evolving static solution for $p=5$.