A possibility to produce bound states of several heavy fermions, which are bound together due to the Higgs exchange, is examined. It is shown that for 12 fermions, 6 fermions, and 6 antifermions, occupying the lowest $S_{1/2}$ shell this bound state cannot exist if the fermion mass is below the critical value $m_{\mathrm{cr}}$, which depends on the Higgs mass and is found to be restricted to $320<m_{\mathrm{cr}}<410\mathrm{GeV}/c^2$ for the Higgs mass $m_{\mathrm{H}}$ in the interval $100\le m_{\mathrm{H}}\le 200\mathrm{GeV}/c^2$. This estimate is derived in the relativistic mean-field approximation. The corrections produced by the omitted effects are estimated to be not able to reduce the critical value for the fermion mass significantly.

Phase transitions in charged topological black holes dressed with a scalar field are studied. These black holes are solutions of the Einstein-Maxwell theory with a negative cosmological constant and a conformally coupled real self-interacting scalar field. Comparing, in the grand canonical ensemble, the free energies of the hairy and undressed black holes two different phase transitions are found. The first of them is one of second-order type and it occurs at a temperature defined by the value of the cosmological constant. Below this temperature an undressed black hole spontaneously acquires a scalar hair. The other phase transition is one of first-order type. The corresponding critical temperature, which is bounded from above by the one of the previous case, strongly depends on the coupling constant of the quartic self-interaction potential, and this transition only appears when the coupling constant is less than a certain value. In this case, below the critical temperature the undressed black hole is thermodynamically favored. However, when the temperature exceeds the critical value a hairy black hole is likely to be occur.

We study the high-energy limit of tree-level string production amplitudes from decaying D-branes in bosonic string theory, interpreting the vertex operators as external charges interacting with a Coulomb gas corresponding to the rolling tachyon background, and performing an electrostatic analysis. In particular, we consider two open string–one closed string amplitudes and four open string amplitudes, and calculate explicit formulas for the leading exponential behavior.

One-electron $3+1$ and $2+1$ Dirac equations are used to calculate the motion of a relativistic electron in a vacuum in the presence of an external magnetic field. First, calculations are carried on an operator level and exact analytical results are obtained for the electron trajectories which contain both intraband frequency components, identified as the cyclotron motion, as well as interband frequency components, identified as the trembling motion, Zitterbewegung (ZB). Next, time-dependent Heisenberg operators are used for the same problem to compute average values of electron position and velocity employing Gaussian wave packets. It is shown that the presence of a magnetic field and the resulting quantization of the energy spectrum has pronounced effects on the electron ZB: it introduces intraband frequency components into the motion, influences all the frequencies, and makes the motion stationary (not decaying in time) in case of the $2+1$ Dirac equation. Finally, simulations of the $2+1$ Dirac equation and the resulting electron ZB in the presence of a magnetic field are proposed and described employing trapped ions and laser excitations. Using simulation parameters achieved in recent experiments of Gerritsma and coworkers, we show that the effects of the simulated magnetic field on ZB are considerable and can certainly be observed.

We discuss aspects of the monopole-vortex complex soliton arising in a hierarchically broken gauge system, $G\to H\to \mathbb{1}$, in a $\theta$ vacuum of the underlying $G$ theory. Here we focus our attention mainly on the simplest such system with $G=SU(2)$ and $H=U(1)$. A consistent picture of the effect of the $\theta$ parameter is found both in a macroscopic, dual picture and in a microscopic description of the monopole-vortex complex soliton.

In this work we present two correspondences between the massless Gross-Neveu model with one or two coupling constants in $1+1$ dimensions and nonrelativistic field theories in $3+1$ dimensions. It is shown that on a mean-field level the massless Gross-Neveu model can be mapped onto BCS theory provided that translational invariance of the condensate is assumed. The generalized massless Gross-Neveu model with two coupling constants is mapped onto a quasi one-dimensional extended Hubbard model used in the description of spin-Peierls systems. It is shown that the particle hole symmetry of the Hubbard model implies self-consistency of the condensate. The dimensional reduction allows an identification of the phase diagrams of the models.

In this paper I determine the general form of the physical and mathematical restrictions that arise on the interactions of gravity and scalar fields in the 2T field theory setting, in $d+2$ dimensions, as well as in the emerging shadows in $d$ dimensions. These constraints on scalar fields follow from an underlying $\mathrm{Sp}(2,R)$ gauge symmetry in phase space. Determining these general constraints provides a basis for the construction of 2T supergravity, as well as physical applications in 1T-field theory, that are discussed briefly here and more detail elsewhere. In particular, no scale models that lead to a vanishing cosmological constant at the classical level emerge naturally in this setting.

Naked singularities are hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon. Penrose has proposed a conjecture, according to which there exists a cosmic censor who forbids the occurrence of naked singularities. Distinguishing between astrophysical black holes and naked singularities is a major challenge for present day observational astronomy. In the context of stationary and axially symmetrical geometries, a possibility of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around rotating naked singularities and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around axially-symmetric rotating naked singularities, obtained as solutions of the field equations in the Einstein-massless scalar field theory. A first major difference between rotating naked singularities and Kerr black holes is in the frame dragging effect, the angular velocity of a rotating naked singularity being inversely proportional to its spin parameter. Because of the differences in the exterior geometry, the thermodynamic and electromagnetic properties of the disks (energy flux, temperature distribution and equilibrium radiation spectrum) are different for these two classes of compact objects, consequently giving clear observational signatures that could discriminate between black holes and naked singularities. For specific values of the spin parameter and of the scalar charge, the energy flux from the disk around a rotating naked singularity can exceed by several orders of magnitude the flux from the disk of a Kerr black hole. In addition to this, it is also shown that the conversion efficiency of the accreting mass into radiation by rotating naked singularities is always higher than the conversion efficiency for black holes, i.e., naked singularities provide a much more efficient mechanism for converting mass into radiation than black holes. Thus, these observational signatures may provide the necessary tools from clearly distinguishing rotating naked singularities from Kerr-type black holes.

We initiate a quantitative exploration of the entire landscape. Predictions thus far have focused on subsets of landscape vacua that share most properties with our own. Using the entropic principle (the assumption that entropy production traces the formation of complex structures such as observers), we derive six predictions that apply to the whole landscape. Typical observers find themselves in a flat Universe, at the onset of vacuum domination, surrounded by a recently produced bath of relativistic quanta. These quanta are neither very dilute nor condensed, and thus appear as a roughly thermal background. Their characteristic wavelength is of order the inverse fourth root of the vacuum energy. These predictions hold for completely arbitrary observers, in arbitrary vacua with potentially exotic particle physics and cosmology. They agree with observation: We live in a flat Universe at the onset of vacuum domination, whose dominant entropy production process (the glow of galactic dust) has recently produced a radiation bath (the cosmic infrared background). This radiation is marginally dilute, relativistic, and has a wavelength of order 100 microns, as predicted.

We analyze infrared divergences arising in calculations involving light and massless fields in de Sitter space. We show that these arise from an incorrect treatment of the constant mode of the field and that a correct quantization leads to a well-defined and calculable perturbation expansion. We illustrate this by computing the first nontrivial loop correction in a theory of a massless scalar field with a quartic interaction.

We consider constraints on a phenomenological dark-matter model consisting of two nearly degenerate particle species using observed properties of the Milky Way satellite galaxy population. The two parameters of this model, assuming the particle masses are $\gtrsim \mathrm{GeV}$, are $v_{\mathrm{k}}$, the recoil speed of the daughter particle, and $\tau$, the lifetime of the parent particle. The satellite constraint that spans the widest range of $v_{\mathrm{k}}$ is the number of satellites that have a mass within 300 pc ${\mathrm{M}}_{300}>5\times {10}^6{\mathrm{M}}_{\odot }$, although constraints based on ${\mathrm{M}}_{300}$ in the classical dwarfs and the overall velocity function are competitive for $v_{\mathrm{k}}\gtrsim 50\mathrm{km}{\mathrm{s}}^{-1}$. In general, we find that $\tau \lesssim 30\mathrm{Gyr}$ is ruled out for $20\mathrm{km}{\mathrm{s}}^{-1}\lesssim v_{\mathrm{k}}\lesssim 200\mathrm{km}{\mathrm{s}}^{-1}$, although we find that the limits on $\tau$ for fixed $v_{\mathrm{k}}$ can change by a factor of $\sim 3$ depending on the star-formation histories of the satellites. We advocate using the distribution of ${\mathrm{M}}_{300}$ in Milky Way satellites, determined by next-generation all-sky surveys and follow-up spectroscopy, as a probe of dark-matter physics.

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabaticlike scalar perturbation mode that evolves passively thereafter (called the passive mode). We compute the CMB reduced bispectrum ($B_{L_1{L}_2{L}_3}$) induced by this passive mode, sourced via the Sachs-Wolfe effect, on large angular scales. For any configuration of bispectrum, taking a partial sum over mode-coupling terms, we find a typical value of $l_1(l_1+1)l_3(l_3+1)b_{l_1{l}_2{l}_3}\sim 6-9\times {10}^{-16}$, for a magnetic field of $B_0\sim 3\mathrm{nG}$, assuming a nearly scale-invariant magnetic spectrum. We also evaluate, in full, the bispectrum for the squeezed collinear configuration over all angular mode-coupling terms and find $l_1(l_1+1)l_3(l_3+1)b_{l_1{l}_2{l}_3}\approx -1.4\times {10}^{-16}$. These values are more than $\sim {10}^6$ times larger than the previously calculated magnetic compensated scalar mode CMB bispectrum. Observational limits on the bispectrum from WMAP7 data allow us to set upper limits of $B_0\sim 2\mathrm{nG}$ on the present value of the cosmic magnetic field of primordial origin. This is over 10 times more stringent than earlier limits on $B_0$ based on the compensated mode bispectrum.

We analyze whether or not Lifshitz field theories in $4+1$ dimensions may provide ultraviolet-complete domain-wall–brane models. We first show that Lifshitz scalar-field theory can admit topologically stable domain-wall solutions. A Lifshitz fermion field is then added to the toy model, and we demonstrate that $3+1$-dimensional Kaluza-Klein zero-mode solutions do not exist when the four spatial dimensions are treated isotropically. To recover $3+1$-dimensional chiral fermions dynamically localized to the domain wall, we must postulate the breaking of full 4-dimensional rotational symmetry down to the subgroup of rotations, which mix the usual 3-dimensional spatial directions and fix the extra-dimensional axis in addition to the anisotropy between space and time.

We construct and analyze theories with a gauge symmetry in the ultraviolet of the form $G\otimes G_b$, in which the vectorial, asymptotically free $G_b$ gauge interaction becomes strongly coupled at a scale where the $G$ interaction is weakly coupled and produces bilinear fermion condensates that dynamically break the $G$ symmetry. Comparisons are given between Higgs and dynamical symmetry-breaking mechanisms for various models.

We consider a new possibility of incorporating chiral symmetry breaking in soft wall models with a quadratic dilaton and AdS metric. In particular, we allow the mass of the scalar modes propagating in the bulk to have a dependence on the holographical coordinate. In one of the models that we discuss, it is possible obtain a good meson spectra considering current quark masses, and in the other two models considered, good results can be obtained at the expense of considering rather large quark masses.

If a TeV-scale charged gauge boson ($W^{\prime }$) is discovered at the Large Hadron Collider (LHC), it will become imperative to determine its chiral couplings to standard model (SM) fermions in order to learn about the underlying theory containing the $W^{\prime }$. We describe the reconstruction of the $tb$ decay mode of the $W^{\prime }$ at the LHC, and identify various kinematic observables such as the angular distributions of the top quark and the lepton resulting from top decay that can be used to disentangle the chiral couplings of the $W^{\prime }$ to SM fermions. We demonstrate by presenting analytical expressions, numerical simulations, as well as intuitive illustrations for these observables at the LHC that among the SM fermions, the polarized top quark can most directly probe the chirality of such couplings.

We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the regularization independent momentum or RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular, with recent two-loop calculations.

Parton distribution functions, which describe probability densities of quarks and gluons in the proton, are essential for interpreting the data from high energy hadron colliders. The parton distribution functions are measured by approximating them with functional forms that contain many adjustable parameters, which are determined by fitting a wide variety of experimental data. This paper examines the uncertainty that arises from choosing the form of parametrization, and shows how that uncertainty can be reduced using a technique based on Chebyshev polynomials.