We investigate resolutions of heterotic orbifolds using toric geometry. Our starting point is provided by the recently constructed heterotic models on explicit blowup of ${\mathbb{C}}^n/{\mathbb{Z}}_n$ singularities. We show that the values of the relevant integrals, computed there, can be obtained as integrals of divisors (complex codimension one hypersurfaces) interpreted as (1, 1)-forms in toric geometry. Motivated by this we give a self-contained introduction to toric geometry for nonexperts, focusing on those issues relevant for the construction of heterotic models on toric orbifold resolutions. We illustrate the methods by building heterotic models on the resolutions of ${\mathbb{C}}^2/{\mathbb{Z}}_3$, ${\mathbb{C}}^3/{\mathbb{Z}}_4$, and ${\mathbb{C}}^3/{\mathbb{Z}}_2\times {\mathbb{Z}}_2^{\prime }$. We are able to obtain a direct identification between them and the known orbifold models. In the ${\mathbb{C}}^3/{\mathbb{Z}}_2\times {\mathbb{Z}}_2^{\prime }$ case we observe that, in spite of the existence of two inequivalent resolutions, fully consistent blowup models of heterotic orbifolds can only be constructed on one of them.

We construct a simple local model of dynamical supersymmetry breaking. The model is a one-generation $SU(5)$ that arises from a IIB ${\mathbb{Z}}_N$ orientifold. It does not admit a runaway direction and is argued to stabilize the blowup mode related to the corresponding $U(1)$ factor. The theory demonstrates the existence of a new class of “blowup” fractional branes

We discuss the signatures of the transition from galactic to extragalactic cosmic rays in different scenarios, giving the most attention to the dip scenario. The dip is a feature in the diffuse spectrum of ultrahigh-energy protons in the energy range $1\times {10}^{18}–4\times {10}^{19}\mathrm{eV}$, which is caused by electron-positron pair production on the cosmic microwave background radiation. The dip scenario provides a simple physical description of the transition from galactic to extragalactic cosmic rays. Here we summarize the signatures of the pair-production dip model for the transition, most notably the spectrum, the anisotropy, and the chemical composition. The main focus of our work is, however, on the description of the features that arise in the elongation rate and in the distribution of the depths of shower maximum $X_{\max }$ in the dip scenario. We find that the curve for $X_{\max }(E)$ shows a sharp increase with energy, which reflects a sharp transition from an iron-dominated flux at low energies to a proton-dominated flux at $E\sim {10}^{18}\mathrm{eV}$. We also discuss in detail the shape of the $X_{\max }$ distributions for cosmic rays of given energy and demonstrate that this represents a powerful tool to discriminate between the dip scenario and other possible models of the transition.

We find the full spectrum of fermion bound states on a $Z_2$ kink. In addition to the zero mode, there are $\mathrm{int}[2m_f/m_s]$ bound states, where $m_f$ is the fermion and $m_s$ the scalar mass. We also study fermion modes on the background of a well-separated kink-antikink pair. Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, $2L$, and faster than $e^{-a2L}$ where $a=\min (m_s,2m_f)$. By numerical evaluation, we find some of the low lying bound states explicitly.

We have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in its most simple form; the generalization to electromagnetic fields is outlined in Ref. [T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Phys. Rev. Lett. 99, 170403 (2007).]. The interaction between the objects is attributed to quantum fluctuations of source distributions on their surfaces, which we decompose in terms of multipoles. A functional integral over the effective action of multipoles gives the resulting interaction. Each object’s shape and boundary conditions enter the effective action only through its scattering matrix. Their relative positions enter through universal translation matrices that depend only on field type and spatial dimension. The distinction of our method from the pairwise summation of two-body potentials is elucidated in terms of the scattering processes between three objects. To illustrate the power of the technique, we consider Robin boundary conditions $\varphi -\lambda {\partial }_n\varphi =0$, which interpolate between Dirichlet and Neumann cases as $\lambda$ is varied. We obtain the interaction between two such spheres analytically in a large separation expansion, and numerically for all separations. The cases of unequal radii and unequal $\lambda$ are studied. We find sign changes in the force as a function of separation in certain ranges of $\lambda$ and see deviations from the proximity force approximation even at short separations, most notably for Neumann boundary conditions.

We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon-crossing time is smaller than some critical value ($\sim |$ slow-roll parameter ${|}^{-1}$), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.

In addition to the boosted static solution there are two other classes of stationary stringlike solutions of the vacuum Einstein equation in ($4+1$) dimensions. Each class is characterized by three parameters of mass, tension, and momentum flow along the fifth coordinate. We analyze the metric properties of one of the two classes, which was previously assumed to be naked singular, and show that the solution spectrum contains black string and wormhole in addition to the known naked singularity as the momentum flow to mass ratio increases. Interestingly, there does not exist new zero momentum solution in these cases.

We investigate the non-Gaussianity of primordial curvature perturbations in the modulated reheating scenario where the primordial perturbation is generated due to the spatial fluctuation of the rate of the inflaton decay to radiation. We use the $\delta N$ formalism to evaluate the trispectrum of the curvature perturbation as well as its bispectrum. We give expressions for three nonlinear parameters $f_{\mathrm{NL}}$, ${\tau }_{\mathrm{NL}}$, and $g_{\mathrm{NL}}$ in the modulated reheating scenario. If both the intrinsic non-Gaussianity of scalar field fluctuations and third derivative of the decay rate with respect to the scalar fields are negligibly small, $g_{\mathrm{NL}}$ has at least the same order of magnitude as $f_{\mathrm{NL}}$. We also give a general inequality between $f_{\mathrm{NL}}$ and ${\tau }_{\mathrm{NL}}$, which is true for other inflationary scenarios as long as the primordial non-Gaussianity comes from superhorizon evolution.

While the bino-dominated lightest neutralino of the minimal supersymmetric standard model (MSSM) is an interesting and widely studied candidate of dark matter, the $p$-wave suppression of its annihilation cross section requires fine-tuning of the MSSM spectra to be consistent with Wilkinson Microwave Anisotropy Probe (WMAP) observations. We propose a pseudo-Dirac bino that arises in theories with D-type supersymmetry breaking as an intriguing alternative candidate of dark matter. The pseudo-Dirac nature of the bino gives a natural mechanism of enhanced coannihilation because these two states are degenerate in the absence of electroweak symmetry breaking. In addition, the lightest state can be consistent with limits of direct-detection experiments because of the lack of vector interactions, as with the case of the MSSM bino.

For the gluon propagator of pure $SU(2)$ lattice gauge theory in the Landau gauge we investigate the effect of Gribov copies and finite-volume effects. Concerning gauge fixing, we enlarge the accessible gauge orbits by adding nonperiodic $\mathbb{Z}(2)$ gauge transformations and systematically employ the simulated annealing algorithm. Strategies to keep all $\mathbb{Z}(2)$ sectors under control within reasonable CPU time are discussed. We demonstrate that the finite-volume effects in the infrared regime become ameliorated. Reaching a physical volume of about $(6.5\mathrm{fm}{)}^4$, we find that the propagator, calculated with the indicated improvements, becomes flat in the region of smallest momenta. There are first signs in four dimensions of a decrease towards vanishing momentum.

We present results for the QCD equation of state, quark densities, and susceptibilities at nonzero chemical potential, using $2+1$ flavor asqtad ensembles with $N_t=4$. The ensembles lie on a trajectory of constant physics for which $m_{ud}\approx 0.1m_s$. The calculation is performed using the Taylor expansion method with terms up to sixth order in $\mu /T$.

We use chiral perturbation theory to study the extraction of pion electromagnetic polarizabilities from lattice QCD. Chiral extrapolation formulae are derived for partially quenched QCD, and quenched QCD simulations. On a torus, volume dependence of electromagnetic current correlators is complicated by $SO(4)$ breaking, as well as photon zero-mode interactions. We determine finite volume corrections to the Compton scattering tensor of pions. We argue, however, that such results cannot be used to ascertain volume corrections to polarizabilities determined in lattice QCD with background field methods. Connection is lacking because small momentum expansions are not permitted in finite volume. Our argument also applies to form factors. Volume effects for background field calculations of electromagnetic moments cannot be deduced from finite volume form factors.

We study quarkonium correlators and spectral functions at zero and finite temperature in QCD with only heavy quarks using potential models combined with perturbative QCD. First, we show that this approach can describe the quarkonium correlation function at zero temperature. Using a class of screened potentials based on lattice calculations of the static quark-antiquark free energy we calculate spectral functions at finite temperature. We find that all quarkonium states, with the exception of the $1S$ bottomonium, dissolve in the deconfined phase at temperatures smaller than $1.5T_c$, in contradiction with the conclusions of recent studies. Despite this the temperature dependence of the quarkonium correlation functions calculated on the lattice is well reproduced in our model. We also find that even in the absence of resonances the spectral function at high temperatures is significantly enhanced over the spectral function corresponding to free quark-antiquark propagation.

On the basis of the three fundamental principles of (i) Poincaré symmetry of space-time, (ii) electromagnetic gauge symmetry, and (iii) unitarity, we construct an universal Lagrangian for the electromagnetic interactions of elementary vector particles, i.e., massive spin-1 particles transforming in the $(\frac{1}{2},\frac{1}{2})$ representation space of the homogeneous Lorentz group. We make the point that the first two symmetries alone do not fix the electromagnetic couplings uniquely but solely prescribe a general Lagrangian depending on two free parameters, here denoted by $\xi$ and $g$. The first one defines the electric-dipole and the magnetic-quadrupole moments of the vector particle, while the second determines its magnetic-dipole and electric-quadrupole moments. In order to fix the parameters one needs an additional physical input suited for the implementation of the third principle. As such, one chooses Compton scattering off a vector target and requires the cross section to respect the unitarity bounds in the high-energy limit. As a result, we obtain the universal $g=2$ and $\xi =0$ values which completely characterize the electromagnetic couplings of the considered elementary vector field at tree level. The nature of this vector particle, Abelian versus non-Abelian, does not affect this structure. Merely, a partition of the $g=2$ value into non-Abelian, $g_{na}$, and Abelian, $g_a=2-g_{na}$, contributions occurs for non-Abelian fields with the size of $g_{na}$ being determined by the specific non-Abelian group appearing in the theory of interest, be it the standard model or any other theory.

We report measurements of the exclusive cross section for $e^{+}{e}^{-}\to D\overline{D}$, where $D=D^0$ or $D^{+}$, in the center-of-mass energy range from the $D\overline{D}$ threshold to 5 GeV with initial-state radiation. The analysis is based on a data sample collected with the Belle detector with an integrated luminosity of $673{\mathrm{fb}}^{-1}$.

In this paper, we apply the statefinder diagnostic to the cosmology with the abnormally weighting energy hypothesis (AWE cosmology), in which dark energy in the observational (ordinary matter) frame results from the violation of the weak equivalence principle by pressureless matter. It is found that there exist closed loops in the statefinder plane, which is an interesting characteristic of the evolution trajectories of statefinder parameters and can be used to distinguish AWE cosmology from other cosmological models.

The Hamiltonian formulation of superfluids based on noncanonical Poisson brackets is studied in detail. The assumption that the momentum density is proportional to the flow of the conserved energy is shown to lead to the covariant relativistic theory previously suggested by Khalatnikov, Lebedev, and Carter, and some potentials in this theory are given explicitly. We discuss hydrodynamic fluctuations in the presence of dissipative effects, and we derive the corresponding set of hydrodynamic correlation functions. Kubo relations for the transport coefficients are obtained.

The physical process version of the first law for black holes states that the passage of energy and angular momentum through the horizon results in a change in area $\frac{\kappa }{8\pi }\Delta A=\Delta E-\Omega \Delta J$, so long as this passage is quasistationary. A similar physical process first law can be derived for any bifurcate Killing horizon in any spacetime dimension $d\ge 3$ using much the same argument. However, to make this law nontrivial, one must show that sufficiently quasistationary processes do in fact occur. In particular, one must show that processes exist for which the shear and expansion remain small, and in which no new generators are added to the horizon. Thorne, MacDonald, and Price considered related issues when an object falls across a $d=4$ black hole horizon. By generalizing their argument to arbitrary $d\ge 3$ and to any bifurcate Killing horizon, we derive a condition under which these effects are controlled and the first law applies. In particular, by providing a nontrivial first law for Rindler horizons, our work completes the parallel between the mechanics of such horizons and those of black holes for $d\ge 3$. We also comment on the situation for $d=2$.

Tensor-vector-scalar (TeVeS) theory, a relativistic theory of gravity, was designed to provide a basis for the modified Newtonian dynamics. Since TeVeS differs from general relativity (e.g., it has two metrics, an Einstein metric and a physical metric), black hole solutions of it would be valuable for a number of endeavors ranging from astrophysical modeling to investigations into the interrelation between gravity and thermodynamics. Giannios has recently found a TeVeS analogue of the Schwarzschild black hole solution. We proceed further with the program by analytically solving the TeVeS equations for a static spherically symmetric and asymptotically flat system of electromagnetic and gravity fields. We show that one solution is provided by the Reissner-Nordström metric as physical metric, the TeVeS vector field pointing in the time direction, and a TeVeS scalar field positive everywhere (the last feature protects from superluminal propagation of disturbances in the fields). We work out black hole thermodynamics in TeVeS using the physical metric; black hole entropy, temperature, and electric potential turn out to be identical to those in general relativity. We find it inconsistent to base thermodynamics on the Einstein metric. In light of this, we reconsider the Dubovsky-Sibiryakov scenario for violating the second law of thermodynamics in theories with Lorentz symmetry violation.

We suggest a modification of the Barrett-Crane spin foam model of four-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrett-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the $B$ field (bivectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of the Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barrett-Crane model.