Combining the effects of fluxes and gaugino condensation in heterotic supergravity, we use a ten-dimensional approach to find a new class of four-dimensional supersymmetric ${\mathrm{AdS}}_4$ compactifications on almost-Hermitian manifolds of $SU(3)$ structure. Computation of the torsion allows a classification of the internal geometry, which for a particular combination of fluxes and condensate, is nearly Kähler. We argue that all moduli are fixed, and we show that the Kähler potential and superpotential proposed in the literature yield the correct ${\mathrm{AdS}}_4$ radius. In the nearly Kähler case, we are able to solve the $H$ Bianchi identity using a nonstandard embedding. Finally, we point out subtleties in deriving the effective superpotential and understanding the heterotic supergravity in the presence of a gaugino condensate.

To describe a massive graviton in 4D Minkowski space-time one introduces a quadratic term in the Lagrangian. This term, however, can lead to a readjustment or instability of the background instead of describing a massive graviton on flat space. We show that for all local 4D Lorentz-invariant mass terms Minkowski space is unstable. The instability can develop in a time scale that is many orders of magnitude shorter than the inverse graviton mass. We start with the Pauli-Fierz (PF) term that is the only local mass term with no ghosts in the linearized approximation. We show that nonlinear completions of the PF Lagrangian give rise to instability of Minkowski space. We continue with the mass terms that are not of a PF type. Although these models are known to have ghosts in the linearized approximations, nonlinear interactions can lead to background change in which the ghosts are eliminated. In the latter case, however, the graviton perturbations on the new background are not massive. We argue that a consistent theory of a massive graviton on flat space can be formulated in theories with extra dimensions. They require an infinite number of fields or nonlocal description from a 4D point of view.

We investigate the existence of Taub-NUT (Newman-Unti-Tamburino) and Taub-bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in $d$ dimensions. We find that for all nonextremal NUT solutions of Einstein gravity having no curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter $\alpha$ goes to zero. Furthermore there are no NUT solutions in Gauss-Bonnet gravity that yield nonextremal NUT solutions to Einstein gravity having a curvature singularity at $r=N$ in the limit $\alpha \to 0$. Indeed, we have nonextreme NUT solutions in $2+2k$ dimensions with nontrivial fibration only when the $2k$-dimensional base space is chosen to be ${\mathbb{C}\mathbb{P}}^{2k}$. We also find that the Gauss-Bonnet gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a two-dimensional factor space of positive curvature. Indeed, when the base space has at most one positively curved two-dimensional space as one of its factor spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces of zero or positive constant curvature. The only case for which one does not have bolt solutions is in the absence of a cosmological term with zero curvature base space.

Conditions for the existence and stability of de Sitter space in modified gravity are derived by considering inhomogeneous perturbations in a gauge-invariant formalism. The stability condition coincides with the corresponding condition for stability with respect to homogeneous perturbations, while this is not the case in scalar-tensor gravity. The stability criterion is applied to various modified gravity models of the early and the present universe.

Recent theories of physics beyond the standard model have predicted deviations from Newtonian gravity at short distances. In order to test these theories, we have a built an apparatus that can measure attonewton-scale forces between gold masses separated by distances on the order of $25\mu \mathrm{m}$. A micromachined silicon cantilever was used as the force sensor, and its displacement was measured with a fiber interferometer. We have used our measurements to set bounds on the magnitude $\alpha$ and length scale $\lambda$ of Yukawa-type deviations from Newtonian gravity; our results presented here yield the best experimental limit in the range of $\lambda =6–20\mu \mathrm{m}$.

We study minimal scenarios of resonant leptogenesis near the electroweak phase transition. These models offer a number of testable phenomenological signatures for low-energy experiments and future high-energy colliders. Our study extends previous analyses of the relevant network of Boltzmann equations, consistently taking into account effects from out of equilibrium sphalerons and single lepton flavors. We show that the effects from single lepton flavors become very important in variants of resonant leptogenesis, where the observed baryon asymmetry in the Universe is created by lepton-to-baryon conversion of an individual lepton number, for example, that of the $\tau$-lepton. The predictions of such resonant $\tau$-leptogenesis models for the final baryon asymmetry are almost independent of the initial lepton-number and heavy neutrino abundances. These models accommodate the current neutrino data and have a number of testable phenomenological implications. They contain electroweak-scale heavy Majorana neutrinos with appreciable couplings to electrons and muons, which can be probed at future $e^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{-}$ high-energy colliders. In particular, resonant $\tau$-leptogenesis models predict sizable $0\nu \beta \beta$ decay, as well as $e$- and $\mu$-number-violating processes, such as $\mu \to e\gamma$ and $\mu \to e$ conversion in nuclei, with rates that are within reach of the experiments proposed by the MEG and MECO collaborations.

We determine the abundance of primordial black holes (PBHs) formed in the context of non-Gaussian models with primordial density perturbations. We consider models with a renormalized ${\chi }^2$ probability distribution function parametrized by the number, $\nu$, of degrees of freedom. We show that if $\nu$ is not too large then the PBH abundance will be altered by several orders of magnitude with respect to the standard Gaussian result obtained in the $\nu \to \infty$ limit. We also study the dependence of the spectral index constraints on the nature of the cosmological perturbations for a power-law primordial power spectrum.

The active mass density in Einstein’s theory of gravitation in the analog of Poisson’s equation in a local inertial system is proportional to $\rho +3p/c^2$. Here $\rho$ is the density of energy and $p$ its pressure for a perfect fluid. By using exact solutions of Einstein’s field equations in the static case we study whether the pressure term contributes towards the mass.

The coupling between a primordial magnetic field and the cosmic axion field generates a helical component of the magnetic field around the time in which the axion starts to oscillate. If the energy density of the seed magnetic field is comparable to the energy density of the universe at that time, then the resulting magnetic helicity is about $|H_B|\simeq ({10}^{-20}\mathrm{G}{)}^2\mathrm{kpc}$ and remains constant after its generation. As a corollary, we find that the standard properties of the oscillating axion remain unchanged even in the presence of very strong magnetic fields.

The loop level lepton flavor violating signals $\gamma \gamma \to \ell {\ell }^{\prime }$ ($\ell =e$, $\mu$, $\tau$, $\ell \ne {\ell }^{\prime }$) are studied in a scenario of low-energy, $R$-parity conserving, supersymmetric seesaw mechanism within the context of a high-energy photon collider. Lepton flavor violation is due to off-diagonal elements in the left slepton mass matrix induced by renormalization group equations. The average slepton masses $\tilde{m}$ and the off-diagonal matrix elements $\Delta m$ are treated as model-independent free phenomenological parameters in order to discover regions in the parameter space where the signal cross section may be observable. At the energies of the $\gamma \gamma$ option of the future high-energy linear collider the signal has a potentially large standard model background, and therefore particular attention is paid to the study of kinematical cuts in order to reduce the latter to an acceptable level. We find, for the ($e\tau$) channel, non-negligible fractions of the parameter space (${\delta }_{LL}=\Delta m^2/{\tilde{m}}^2\gtrsim {10}^{-1}$) where the statistical significance (SS) is $\mathrm{SS}\gtrsim 3$.

We study the large momentum behavior of the ghost propagator in the quenched SU(3) lattice gauge theory with Wilson action. The study is performed on lattices with a physical volume fixed around 1.6 fm and different lattice spacings: 0.100, 0.070, and 0.055 fm. We implement an efficient algorithm for computing the Faddeev-Popov operator on the lattice. We are able to extrapolate the lattice data for the ghost propagator towards the continuum and to show that the extrapolated data on each lattice can be described up to four-loop perturbation theory from 2.0 to 6.0 GeV. The three-loop values are consistent with those extracted from previous perturbative studies of the gluon propagator. However the effective ${\Lambda }_{\overline{\mathrm{MS}}}$ scale which reproduces the data depends strongly upon the order of perturbation theory and on the renormalization scheme used in the parametrization. We show how the truncation of the perturbative series can account for the magnitude of the dependency in this energy range. The contribution of nonperturbative corrections will be discussed elsewhere.

We show a possibility that a strong “magnetic field” $\sim {10}^{15}\mathrm{G}$ is produced by color ferromagnetic quark matter in neutron stars. In the quark matter a color magnetic field is generated spontaneously owing to the Savvidy mechanism and a gluon condensate arises for the stabilization of the field. Since the quark matter is electrically charged in the neutron stars, the rotation of the quarks around the color magnetic field produces the strong “magnetic field.”

In this work it is investigated if fermionic sources could be responsible for accelerated periods during the evolution of a universe where a matter field would answer for the decelerated period. The self-interaction potential of the fermionic field is considered as a function of the scalar and pseudoscalar invariants. Irreversible processes of energy transfer between the matter and gravitational fields are also considered. It is shown that the fermionic field could behave like an inflaton field in the early universe and as dark energy for an old universe.

We consider a minimal formulation of SO(10) grand unified theory wherein all the fermion masses arise from Yukawa couplings involving one $\overline{\mathbf{126}}$ and one $\mathbf{10}$ of Higgs multiplets. It has recently been recognized that such theories can explain, via the type-II seesaw mechanism, the large ${\nu }_{\mu }-{\nu }_{\tau }$ mixing as a consequence of $b-\tau$ unification at the grand unified theory scale. In this picture, however, the Cabibbo-Kobayashi-Maskawa quark-mixing matrix phase $\delta$ lies preferentially in the second quadrant, in contradiction with experimental measurements. We revisit this minimal model and show that the conventional type-I seesaw mechanism generates phenomenologically viable neutrino masses and mixings, while being consistent with Cabibbo-Kobayashi-Maskawa quark-mixing matrix $CP$ violation. We also present improved fits in the type-II seesaw scenario and suggest fully consistent fits in a mixed scenario.

We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying $SU(2)$ lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison. In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.

A complete basis for the next-to-next-to leading order heavy-to-light currents in the soft-collinear effective theory is constructed. Reparametrization invariance is imposed by deriving constraint equations. Their solutions give the set of allowed Dirac structures as well as relations between the Wilson coefficients of operators that appear at different orders in the power expansion. The completeness of reparametrization invariance constraints derived on a projected surface is investigated. We also discuss the universality of the ultrasoft Wilson line with boundary conditions.

We present a Chern-Simons matrix model describing the fractional quantum Hall effect on the two sphere. We demonstrate the equivalence of our proposal to particular restrictions of the Calogero-Sutherland model, reproduce the quantum states and filling fraction and show the compatibility of our result with the Haldane spherical wave functions.

We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form ${\Sigma }_{\kappa }^n\times {\mathbb{R}}^{+}$, ${\Sigma }_{\kappa }^n$ an $n-$manifold of constant curvature $\kappa$. Linear perturbations for this class of spacetimes can be generally classified into tensor, vector and scalar types. In a previous paper, tensor perturbations were analyzed. In this paper we study vector and scalar perturbations. We show that vector perturbations can be analyzed in general using an $S$-deformation approach and do not introduce instabilities. On the other hand, we show by analyzing an explicit example that, contrary to what happens in Einstein gravity, scalar perturbations may lead to instabilities in black holes with spherical horizons when the Gauss-Bonnet string corrections are taken into account.

A small body moving in the field of a much larger black hole and subjected to its own gravity moves on an accelerated world line in the background spacetime of the large black hole. The acceleration is produced by the body’s gravitational self-force, which is constructed from the body’s retarded gravitational field. The adiabatic approximation to the gravitational self-force is obtained instead from the half-retarded minus half-advanced field. It is much easier to compute, and it is known to produce the same dissipative effects as the true self-force. We argue that the adiabatic approximation is limited, because it discards important conservative terms which lead to the secular evolution of some orbital elements. We argue further that this secular evolution has measurable consequences; in particular, it affects the phasing of the orbit and the phasing of the associated gravitational wave. Our argument rests on a simple toy model involving a point electric charge moving slowly in the weak gravitational field of a central mass; the charge is also subjected to its electromagnetic self-force. In this simple context the true self-force is known explicitly and it can cleanly be separated into conservative and radiation-reaction pieces. Its long-term effect on the particle’s orbital elements can be fully determined. In this model we observe that the conservative part of the self-force produces a secular regression of the orbit’s periapsis. We explain how the conclusions reached on the basis of the toy model can be extended to the gravitational self-force, and we attempt to extend them also to the case of rapid motions and strong fields. While the limitations of the adiabatic approximation are quite severe in a post-Newtonian context in which the motion is slow and the gravitational field weak, they may be less severe for rapid motions and strong fields.

The direction dependence of the WIMP direct detection rate provides a powerful tool for distinguishing a WIMP signal from possible backgrounds. We study the number of events required to discriminate a WIMP signal from an isotropic background for a detector with 2-d readout using nonparametric circular statistics. We also examine the number of events needed to (i) detect a deviation from rotational symmetry, due to flattening of the Milky Way halo and (ii) detect a deviation in the mean direction due to a tidal stream. If the senses of the recoils are measured then of order 20–-70 events (depending on the plane of the 2-d readout and the detector location) will be sufficient to reject isotropy of the raw recoil angles at $90\%$ confidence. If the senses can not be measured these number increase by roughly 2 orders of magnitude (compared with an increase of 1 order of magnitude for the case of full 3-d readout). The distributions of the reduced angles, with the (time-dependent) direction of solar motion subtracted, are far more anisotropic, however, and if the isotropy tests are applied to these angles then the numbers of events required are similar to the case of 3-d readout. A deviation from rotational symmetry will only be detectable if the Milky Way halo is significantly flattened. The deviation in the mean direction due to a tidal stream is potentially detectable, however, depending on the density and direction of the stream. The meridian plane (which contains the Earth’s spin axis) is, for all detector locations, the optimum readout plane for rejecting isotropy. However readout in this plane can not be used for detecting flattening of the Milky Way halo or a stream with direction perpendicular to the galactic plane. In these cases the optimum readout plane depends on the detector location.