Solving instability of the Savvidy vacuum in QCD is a longstanding problem. Using light cone quantization, we analyze the problem not in the real confining vacuum but in dense quark matter where gluons interact weakly with each other. We find a stable ferromagnetic ground state of gluons which carry a single longitudinal momentum. Their states are composed as if they are confined in a two-dimensional quantum well. This supports our previous result that gluons form a quantum Hall state in dense quark matter.

We present a calculation of the quark distribution amplitudes (DAs), the Gegenbauer moments, and decay constants for $\pi$, $\rho$, $K$, and $K^{*}$ mesons using the light-front quark model. While the quark DA for $\pi$ is somewhat broader than the asymptotic one, that for $\rho$ meson is very close to the asymptotic one. The quark DAs for $K$ and $K^{*}$ show asymmetric form due to the flavor SU(3)-symmetry breaking effect. The decay constants for the transversely polarized $\rho$ and $K^{*}$ mesons ($f_{\rho }^T$ and $f_{K^{*}}^T$) as well as the longitudinally polarized ones ($f_{\rho }$ and $f_{K^{*}}$) are also obtained. Our averaged values for $f_V^T/f_V$, i.e. $(f_{\rho }^T/f_{\rho }{)}_{\mathrm{av}}=0.78$ and $(f_{K^{*}}^T/f_{K^{*}}{)}_{\mathrm{av}}=0.84$, are found to be consistent with other model predictions. Especially, our results for the decay constants are in good agreement with the SU(6) symmetry relation, $f_{\rho (K^{*})}^T=(f_{\pi (K)}+f_{\rho (K^{*})})/2$.

We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in E. Silverstein, Phys. Rev. D 73, 086004 (2006).. Milnor’s theorem relates negative sectional curvature on a compact Riemannian manifold to exponential growth of its fundamental group, which translates in string theory to a higher effective central charge arising from winding strings. This exponential density of winding modes is related by modular invariance to the infrared small perturbation spectrum. Using self-consistent approximations valid at large radius, we analyze this correspondence explicitly in a broad set of time-dependent solutions, finding precise agreement between the effective central charge and the corresponding infrared small perturbation spectrum. This indicates a basic relation between geometry, topology, and dimensionality in string theory.

In their minimal form both supersymmetric and smooth hybrid inflation yield a scalar spectral index $n_s$ close to 0.98, to be contrasted with the result $n_s={0.951}_{-0.019}^{+0.015}$ from WMAP3. To realize better agreement, following Bastero-Gil, King, and Shafi, we extend the parameter space of these models by employing a nonminimal Kähler potential. We also discuss nonthermal leptogenesis by inflaton decay and obtain new bounds in these models on the reheat temperature to explain the observed baryon asymmetry.

The spectrum of $\overline{q}q$ mesons in a model where the only interaction is a linear Coulomb-like instantaneous confining potential is studied. The single-quark Green function as well as the dynamical chiral symmetry breaking are obtained from the Schwinger-Dyson (gap) equation. Given the dressed quark propagator, a complete spectrum of “usual” mesons is obtained from the Bethe-Salpeter equation. The spectrum exhibits restoration of chiral and $U(1{)}_A$ symmetries at large spins and/or radial excitations. This property is demonstrated both analytically and numerically. At large spins and/or radial excitations higher degree of degeneracy is observed, namely, all states with the given spin fall into reducible representations $[(0,1/2)\oplus (1/2,0)]\times [(0,1/2)\oplus (1/2,0)]$ that combine all possible chiral multiplets with the given $J$ and $n$. The structure of the meson wave functions as well as the form of the angular and radial Regge trajectories are investigated.

We explore the family of fixed points of $T$-duality transformations in three dimensions. For the simplest nontrivial self-duality conditions it is possible to show that, in addition to the spacelike isometry in which the $T$-duality transformation is performed, these backgrounds must be necessarily stationary. This allows us to prove that, for nontrivial string coupling, the low energy bosonic string backgrounds, which are additionally self-T-dual along an isometry direction generated by a constant norm Killing vector, are uniquely described by a two-parametric class, including only three nonsingular cases: the charged black string, the exact gravitational wave propagating along the extremal black string, and the flat space with a linear dilaton. Besides, for constant string coupling, the only self-T-dual lower energy string background under the same assumptions corresponds to the Coussaert-Henneaux spacetime. Thus, we identify minimum criteria that yield a classification of these quoted examples and only these. All these $T$-dual fixed points describe exact backgrounds of string theory.

Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view of deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the Becchi-Rouet-Stora (BRS) invariance and it is found that there exists two forms of invariance—invariance under the standard BRS transform and under a second, nonstandard transform. The field equations of motion and symmetries are derived explicitly and certain exact relations that simplify the formalism are presented. It is shown that the Ward-Takahashi identity arising from invariance under the nonstandard part of the BRS transform is guaranteed by the functional equations of motion. The Feynman rules and the general decomposition of the two-point Green’s functions are derived. The propagator Dyson-Schwinger equations are derived and certain aspects (energy independence of ghost Green’s functions and the cancellation of energy divergences) are discussed.

We investigate the worldvolume theory that describes $N$ coincident M2-branes ending on an M5-brane. We argue that the fields that describe the transverse spacetime coordinates take values in a nonassociative algebra. We postulate a set of supersymmetry transformations and find that they close into a novel gauge symmetry. We propose a three-dimensional $N=2$ supersymmetric action to describe the truncation of the full theory to the scalar and spinor fields, and show how a Basu-Harvey fuzzy funnel arises as the Bogomol’nyi-Prasad-Sommerfield solution to this theory.

We study next-to-leading-order contributions to the soft static fermion dispersion relation in hot QED. We derive an expression for the complete next-to-leading-order contribution to the retarded fermion self-energy. The real and imaginary parts of this expression give the next-to-leading-order contributions to the mass and damping rate of the fermionic quasiparticle. Many of the terms that are expected to contribute according to the traditional power counting argument are actually subleading. We explain why the power counting method over estimates the contribution from these terms. For the electron damping rate in QED we obtain: ${\gamma }_{\mathrm{QED}}=\frac{e^{2}T}{4\pi }(2.70)$. We check our method by calculating the next-to-leading-order contribution to the damping rate for the case of QCD with two flavors and three colors. Our result agrees with the result obtained previously in the literature. The numerical evaluation of the nlo contribution to the mass is left to a future publication.

In this work we propose a modified gravity with the action $f(R)=\sqrt{R^2-R_0^2}$ instead of the Einstein-Hilbert action to describe the late time acceleration of the Universe. We obtain the equation of the modified gravity both in the metric and Palatini formalisms. An asymptotic solution of gravity equations corresponding to a constant Ricci scalar causes a late time acceleration of the Universe. We do a conformal transformation in the action of the modified gravity and obtain the equivalent minimally coupled scalar-tensor gravity. The equivalent Brans-Dicke gravity of this model is also studied. To examine this model with observation, the perihelion precession of the Mercury is compared with our prediction and we put an upper constraint of $R_0<H_0^2$. This range for $R_0$ is also in agreement with the cosmological acceleration at the present time. Finally we show that this action has instability for the small perturbations of the metric in vacuum solution in which adding a quadratic term of Ricci scalar can stabilize it.

We discuss a cosmology in which cold dark matter particles decay into relativistic particles. We argue that such decays could lead naturally to a bulk viscosity in the cosmic fluid. For decay lifetimes comparable to the present Hubble age, this bulk viscosity enters the cosmic energy equation as an effective negative pressure. We investigate whether this negative pressure is of sufficient magnitude to account for the observed cosmic acceleration. We show that a single decaying species in a $\Lambda =0$, flat, dark-matter dominated cosmology can not reproduce the observed magnitude-redshift relation from Type Ia supernovae. However, a delayed bulk viscosity, possibly due to a cascade of decaying particles may be able to account for a significant fraction of the apparent cosmic acceleration. Possible candidate nonrelativistic particles for this scenario include sterile neutrinos or gauge-mediated decaying supersymmetric particles.

Various effects produced by vector perturbations (vortical peculiar velocity fields) of a flat Friedmann-Robertson-Walker background are considered. In the presence of this type of perturbations, the polarization vector rotates. A formula giving the rotation angle is obtained and, then, it is used to prove that this angle depends on both the observation direction and the emission redshift. Hence, rotations are different for distinct quasars and also for the cosmic microwave background (CMB) radiation coming along different directions (from distinct points of the last scattering surface). As a result of these rotations, some correlations could appear in an initially random field of quasar polarization orientations. Furthermore, the polarization correlations of the CMB could undergo alterations. Quasars and CMB maps are both considered in this paper. In the case of linear vector modes with very large spatial scales, the maximum rotation angles appear to be of a few degrees for quasars (located at redshifts $z<2.6$) and a few tenths of degree for the CMB. These last rotations produce contributions to the $B$ mode of the CMB polarization which are too small to be observed with PLANCK (in the near future); however, these contributions are large enough to be observed with the next generation of satellites, which are being designed to detect the small $B$ mode produced by primordial gravitational waves.

We study the potential of a large future weak lensing survey to constrain dark-energy properties by using both the number counts of detected galaxy clusters (sensitive primarily to density fluctuations on small scales) and tomographic shear-shear correlations (restricted to intermediate and large scales). We use the Fisher matrix formalism, assume a flat universe, and parametrize the equation of state of dark energy by $w(a)=w_0+w_a(1-a)$, to forecast the expected statistical errors from either observable, and from their combination. We show that the covariance between these two observables is small, and argue that they can therefore be regarded as independent constraints. We find that, when the number counts and the shear-shear correlations (on angular scales $\ell \le 1000$) are combined, a LSST (Large Synoptic Survey Telescope)–like survey can yield statistical errors on ${\Omega }_{\mathrm{DE}}$, $w_0$, $w_a$ as tight as 0.003, 0.03, 0.1. These values are a factor of 2–25 better than using either observable alone. The results are also about a factor of 2 better than those from combining number counts of galaxy clusters and their power spectrum.

Some of the best bounds on possible Lorentz violation in the electron sector come from observations of high-energy astrophysical phenomena. Using measurements of TeV inverse Compton radiation from a number of sources, we place the first bounds—at the ${10}^{-15}$ level—on seven of the electron $d$ coefficients.

Predictions for light charged hadron production data in the current fragmentation region of deeply inelastic scattering from the H1 and ZEUS experiments are calculated using perturbative quantum chromodynamics at next-to-leading order, and using fragmentation functions obtained by fitting to similar data from $e^{+}{e}^{-}$ reactions. General good agreement is found when the magnitude $Q^2$ of the hard photon’s virtuality is sufficiently large. The discrepancy at low $Q$ and small scaled momentum $x_p$ is reduced by incorporating mass effects of the detected hadron. By performing quark tagging, the contributions to the overall fragmentation from the various quark flavours in the $ep$ reactions are studied and compared to the contributions in $e^{+}{e}^{-}$ reactions. The yields of the various hadron species are also calculated.

We calculate the branching ratios and $CP$-violating asymmetries for $B_s^0\to {\pi }^0{\eta }^{(\prime )}$ decays in the perturbative QCD (pQCD) factorization approach here. We not only calculate the usual factorizable contributions, but also evaluate the nonfactorizable and annihilation type contributions. The pQCD predictions for the $CP$-averaged branching ratios are $\mathrm{BR}(B_s^0\to {\pi }^0\eta )\approx 0.86\times {10}^{-7}$ and $\mathrm{BR}(B_s^0\to {\pi }^0{\eta }^{\prime })\approx 1.86\times {10}^{-7}$. The pQCD predictions for the $CP$-violating asymmetries are $A_{CP}^{\mathrm{dir}}({\pi }^0\eta )\sim -4.5\%$, $A_{CP}^{\mathrm{dir}}({\pi }^0{\eta }^{\prime })\sim -9.1\%$, $A_{CP}^{\mathrm{mix}}({\pi }^0\eta )\sim -0.2\%$, and $A_{CP}^{\mathrm{mix}}({\pi }^0{\eta }^{\prime })\sim 27\%$ but with large errors. The above pQCD predictions can be tested in the forthcoming LHC-b experiments at CERN.

We point out that in inclusive $B\to X_s{\ell }^{+}{\ell }^{-}$ decay an angular decomposition provides a third ($q^2$ dependent) observable sensitive to a different combination of Wilson coefficients than the rate and the forward-backward asymmetry. Since a precise measurement of $q^2$ dependence requires large data sets, it is important to consider the data integrated over regions of $q^2$. We develop a strategy to extract all measurable Wilson coefficients in $B\to X_s{\ell }^{+}{\ell }^{-}$ from a few simple integrated rates in the low $q^2$ region. A similar decomposition in $B\to K^{*}{\ell }^{+}{\ell }^{-}$, together with the $B\to K^{*}\gamma$ rate, also provides a determination of the Wilson coefficients, without reliance on form factor models and without having to measure the zero of the forward-backward asymmetry.

We report a measurement of the top-quark mass, $M_t$, in the dilepton decay channel of $t\overline{t}\to b{\ell }^{\prime +}{\nu }_{{\ell }^{\prime }}\overline{b}{\ell }^{-}{\overline{\nu }}_{\ell }$ using an integrated luminosity of $1.0{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions collected with the CDF II detector. We apply a method that convolutes a leading-order matrix element with detector resolution functions to form event-by-event likelihoods; we have enhanced the leading-order description to describe the effects of initial-state radiation. The joint likelihood is the product of the likelihoods from 78 candidate events in this sample, which yields a measurement of $M_t=164.5\pm 3.9(\mathrm{stat}.)\pm 3.9(\mathrm{syst}.)\mathrm{GeV}/c^2$, the most precise measurement of $M_t$ in the dilepton channel.

We investigate the graviton propagator in the type IIB supergravity background which is dual to 4 dimensional noncommutative gauge theory. We assume that the boundary is located not at the infinity but at the noncommutative scale where the string frame metric exhibits the maximum. We argue that the Neumann boundary condition is the appropriate boundary condition to be adopted at the boundary. We find that the graviton propagator behaves just as that of the 4 dimensional massless graviton. On the other hand, the nonanalytic behaviors of the other Kaluza-Klein modes are not significantly affected by the Neumann boundary condition.

We construct a complete five dimensional quark-lepton symmetric model, with all fields propagating in the bulk. The extra dimension forms an $S^1/Z_2\times Z_2^{\prime }$ orbifold with the zero mode fermions corresponding to standard model quarks localized at one fixed point. Zero modes corresponding to left (right)-chiral leptons are localized at (near) the other fixed point. This localization pattern is motivated by the symmetries of the model. Shifting the right-handed neutrinos and charged leptons slightly from the fixed point provides a new mechanism for understanding the absence of relations of the type $m_e=m_u$ or $m_e=m_d$ in quark-lepton symmetric models. Flavor changing neutral currents resulting from Kaluza-Klein gluon exchange, which typically arise in the quark sector of split fermion models, are suppressed due to the localization of quarks at one point. The separation of quarks and leptons in the compact extra dimension also acts to suppress the proton decay rate. This permits the extra dimension to be much larger than that obtained in a previous construct, with the bound $1/R\gtrsim 30\mathrm{TeV}$ obtained.