We show that it is possible to construct explicit models of electroweak symmetry breaking in which the number of techniflavors needed to enter the conformal phase of the theory is small and weakly dependent on the number of technicolors. Surprisingly, the minimal model with just two (techni)flavors, together with a suitable gauge dynamics, can be made almost conformal. The theories we consider are generalizations of orientifold-type gauge theories, in which the fermions are in either two-index symmetric or antisymmetric representation of the gauge group, as the underlying dynamics responsible for the spontaneous breaking of the electroweak symmetry. We first study their phase diagram and use the fact that specific sectors of these theories can be mapped into supersymmetric Yang-Mills theory to strengthen our results. This correspondence allows us also to have information on part of the nonperturbative spectrum. We propose and investigate some explicit models while briefly exploring relevant phenomenological consequences. Our theories can not only be tested at the next collider experiments but, due to their simple structure, can also be studied via current lattice simulations.

Whether or not a system is unitary can be seen from the way it, if perturbed, relaxes back to equilibrium. The relaxation of a semiclassical black hole can be described in terms of a correlation function which exponentially decays with time. In the momentum space it is represented by an infinite set of complex poles to be identified with the quasinormal modes. This behavior is in sharp contrast to the relaxation in unitary theory in finite volume: the correlation function of the perturbation in this case is a quasiperiodic function of time and, in general, is expected to show the Poincaré recurrences. In this paper I demonstrate how restore unitarity in the Banados-Teitelboim-Zanelli (BTZ) black hole, the simplest example of an eternal black hole in finite volume. I start with reviewing the relaxation in the semiclassical BTZ black hole and how this relaxation is mirrored in the boundary conformal field theory as suggested by the anti-de Sitter/conformal field theory correspondence. I analyze the sum over $SL(2,\mathbf{Z})$ images of the BTZ space-time and suggest that it does not produce a quasiperiodic relaxation, as one might have hoped, but results in a correlation function which decays by power law. I develop an earlier suggestion and consider a nonsemiclassical deformation of the BTZ space-time that has the structure of a wormhole connecting two asymptotic regions semiclassically separated by a horizon. The small deformation parameter $\lambda$ is supposed to have a nonperturbative origin to capture the finite $N$ behavior of the boundary theory. The discrete spectrum of perturbation in the modified space-time is computed and is shown to determine the expected unitary behavior: the corresponding time evolution is quasiperiodic with a hierarchy of large time scales $\ln 1/\lambda$ and $1/\lambda$ interpreted, respectively, as the Heisenberg and Poincaré time scales in the system.

Higher derivative theory is one of the important models of quantum gravity, renormalizable and asymptotically free within the standard perturbative approach. We consider the $4-ϵ$ renormalization group for this theory, an approach which proved fruitful in $2-ϵ$ models. A consistent formulation in dimension $n=4-ϵ$ requires taking quantum effects of the topological term into account, hence we perform a calculation which is more general than the ones done before. In the special $n=4$ case we confirm a known result by Fradkin, Tseytlin, Avramidi, and Barvinsky, while contributions from a topological term do cancel. In the more general case of $4-ϵ$ renormalization group equations there is an extensive ambiguity related to gauge-fixing dependence. As a result, physical interpretation of these equations is not universal unless we treat $ϵ$ as a small parameter. In the sector of essential couplings one can find a number of new fixed points, but some of them have no analogs in the $n=4$ case.

We investigate the perturbation theory of a fixed-norm, timelike Lorentz-violating vector field. After consistently quantizing the vector field to put constraints on its parameters, we compute the primordial spectra of perturbations generated by inflation in the presence of this vector field. We find that its perturbations are sourced by the perturbations of the inflaton; without the inflaton perturbation the vector field perturbations decay away leaving no primordial spectra of perturbations. Since the inflaton perturbation does not have a spin-$1$ component, the vector field generically does not generate any spin-$1$ “vector-type” perturbations. Nevertheless, it will modify the amplitude of both the spin-$0$ “scalar-type” and spin-$2$ “tensor-type” perturbation spectra, leading to violations of the inflationary consistency relationship.

We study quintessence and phantom field theory models based on linear-negative potentials of the form $V(\varphi )=s\varphi$. We investigate the predicted redshift dependence of the equation of state parameter $w(z)$ for a wide range of slopes $s$ in both quintessence and phantom models. We use the Gold data set of 157 SnIa and place constraints on the allowed range of slopes $s$. We find $s=0\pm 1.6$ for quintessence and $s=\pm 0.7\pm 1$ for phantom models (the range is at the $2\sigma$ level and the units of $s$ are in $\sqrt{3}{M}_{\mathrm{P}}{H}_0^2\simeq {10}^{-38}\mathrm{e}{\mathrm{V}}^3$ where $M_{\mathrm{P}}$ is the Planck mass). In both cases the best fit is very close to $s\simeq 0$ corresponding to a cosmological constant. We also show that specific model independent parametrizations of $w(z)$ which allow crossing of the phantom divide line $w=-1$ (hereafter PDL) provide significantly better fits to the data. Unfortunately such crossings are not allowed in any phantom or quintessence single field model minimally coupled to gravity. Mixed models (coupled phantom-quintessence fields) can in principle lead to a $w(z)$ crossing the PDL but a preliminary investigation indicates that this does not happen for natural initial conditions.

We present a new approach to constructing inflationary models in closed universes. Conformal embedding of closed-universe models in a de Sitter background suggests a quantization condition on the available conformal time. This condition implies that the universe is closed at no greater than the 10% level. When a massive scalar field is introduced to drive an inflationary phase this figure is reduced to closure at nearer the 1% level. In order to enforce the constraint on the available conformal time we need to consider conditions in the universe before the onset of inflation. A formal series around the initial singularity is constructed, which rests on a pair of dimensionless, scale-invariant parameters. For physically acceptable models we find that both parameters are of order unity, so no fine-tuning is required, except in the mass of the scalar field. For typical values of the input parameters we predict the observed values of the cosmological parameters, including the magnitude of the cosmological constant. The model produces a very good fit to the most recent cosmic microwave background (CMB) data. The primordial curvature spectrum provides a possible explanation for the low-$\ell$ falloff in the CMB power spectrum observed by Wilkinson microwave anisotropy probe. The spectrum also predicts a falloff in the matter spectrum at high $k$, relative to a power law. A further prediction of our model is a large tensor mode component, with $r\approx 0.2$.

The nonlinear electrodynamic and gravitational actions on the weak electromagnetic wave propagation in the strong dipole magnetic and gravitational fields of a neutron star are discussed. The eikonal equations for an electromagnetic wave propagating in the external field as well as the motion equations of photons in the dipole magnetic and gravitational fields of a neutron star are obtained from the parametrized post-Maxwellian electrodynamics of the vacuum, which is analogous to the parametrized post-Newtonian theory of gravitation. The solution of these equations indicates that electromagnetic signals, carried by normal waves with mutually orthogonal polarization, travel along different rays and take different time to reach the detector from the same source. It is also shown that in appropriate conditions the value of this nonlinear-electrodynamic lag can be about a tenth part of a microsecond. A detailed analysis of the possibilities of observing this effect by the detection of X-rays and gamma rays from pulsars and magnetars was made.

The so-called time-reversal odd distribution functions are known to be nonvanishing in QCD due to the presence of the link operator in the definition of these quantities. I show that T-odd distributions can be nonvanishing also in chiral models, if vector mesons are introduced as dynamical gauge bosons of a hidden local symmetry. Moreover, since the flavor dependence of these distributions is different in chiral models respect to nonchiral ones, the phenomenological analysis of experimental data will be able to distinguish between these two classes of models.

The effects of the soft gluon emission in hard scattering processes at the phase boundary are resummed in the soft-collinear effective theory (SCET). In SCET, the soft gluon emission is decoupled from the energetic collinear part, and is obtained by the vacuum expectation value of the soft Wilson-line operator. The form of the soft Wilson lines is universal in deep inelastic scattering, in the Drell-Yan process, in the jet production from $e^{+}{e}^{-}$ collisions, and in the ${\gamma }^{*}{\gamma }^{*}\to {\pi }^0$ process, but its analytic structure is slightly different in each process. The anomalous dimensions of the soft Wilson-line operators for these processes are computed along the lightlike path at leading order in SCET and to first order in ${\alpha }_s$, and the renormalization group behavior of the soft Wilson lines is discussed.

In neutral cold quark matter that is sufficiently dense that the strange quark mass $M_s$ is unimportant, all nine quarks (three colors; three flavors) pair in a color-flavor locked (CFL) pattern, and all fermionic quasiparticles have a gap. We recently argued that the next phase down in density (as a function of decreasing quark chemical potential $\mu$ or increasing strange quark mass $M_s$) is the new “gapless CFL” (gCFL) phase in which only seven quasiparticles have a gap, while there are gapless quasiparticles described by two dispersion relations at three momenta. There is a continuous quantum phase transition from CFL to gCFL quark matter at $M_s^2/\mu \approx 2\Delta$, with $\Delta$ the gap parameter. Gapless CFL, like CFL, leaves unbroken a linear combination $\tilde{Q}$ of electric and color charges, but it is a $\tilde{Q}$ conductor with gapless $\tilde{Q}$-charged quasiparticles and a nonzero electron density. In this paper, we evaluate the gapless CFL phase, in several senses. We present the details underlying our earlier work which showed how this phase arises. We display all nine quasiparticle dispersion relations in full detail. Using a general pairing ansatz that only neglects effects that are known to be small, we perform a comparison of the free energies of the gCFL, CFL, two-flavor (2SC), gapless 2SC, and two-flavor up-strange phases. We conclude that as density drops, making the CFL phase less favored, the gCFL phase is the next spatially uniform quark matter phase to occur. A mixed phase made of colored components would have lower free energy if color were a global symmetry, but in QCD such a mixed phase is penalized severely.

Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on a realistic instanton size distribution and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violations and the disappearance of the $0^{-+}$ glueball signal) are traced to their neglect. On the basis of the extended OPE, a comprehensive quantitative analysis of eight Borel-moment sum rules in both spin-0 glueball channels is then performed. The nonperturbative OPE coefficients turn out to be indispensable for consistent sum rules and for their reconciliation with the underlying low-energy theorems. The topological short-distance physics strongly affects the sum rule results and reveals a rather diverse pattern of glueball properties. New predictions for the spin-0 glueball masses and decay constants and an estimate of the scalar glueball width are given, and several implications for glueball structure and experimental glueball searches are discussed.

Inspired by recent measurements with the CLAS detector at Jefferson Lab, we perform a self-consistent analysis of world data on the proton structure function $g_1$ in the range $0.17<Q^2<30(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2$. We compute for the first time low-order moments of $g_1$ and study their evolution from small to large values of $Q^2$. The analysis includes the latest data on both the unpolarized inclusive cross sections and the ratio $R={\sigma }_L/{\sigma }_T$ from Jefferson Lab, as well as a new model for the transverse asymmetry $A_2$ in the resonance region. The contributions of both leading and higher twists are extracted, taking into account effects from radiative corrections beyond the next-to-leading order by means of soft-gluon resummation techniques. The leading twist is determined with remarkably good accuracy and is compared with the predictions obtained using various polarized parton distribution sets available in the literature. The contribution of higher twists to the $g_1$ moments is found to be significantly larger than in the case of the unpolarized structure function $F_2$.

We point out that in models that explain the Los Alamos neutrino scintillation detector result for neutrino oscillations using the mirror neutrinos, the big bang nucleosynthesis constraints on the number of sterile neutrinos can be avoided by using the late time phase transition that only helps to mix the active and the sterile neutrinos. The main idea is to have a standard model singlet scalar field that mixes the visible and the mirror sector and has a low vacuum expectation value ($\sim 100\mathrm{k}\mathrm{e}\mathrm{V}$) so that the active and sterile neutrinos remain unmixed at the big bang nucleosynthesis epoch. The model predicts different effective number of neutrinos at the epoch of recombination compared to the standard model and is therefore testable in experiments that measure cosmic microwave spectrum with a higher precision.

We study possible scalar type interactions in ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$ decay. One finds that an angular distribution asymmetry, $\mathcal{A}(s)$, can be induced from the interference between the scalar part and vector part amplitudes in this decay. Our analysis shows that, in the two-Higgs-doublet model of type II with large $\tan \beta$, the charged Higgs contribution could make $\mathcal{A}(s)$ up to $4\times {10}^{-3}$ without conflict with present experimental constraints. Thus in the future precise experiments in $\tau$-charm factories, this angular distribution asymmetry may be an interesting observable either to be helpful in searching for the signal of the charged Higgs boson or to impose the significant bound on it.

We compute the one-loop string corrections to the Wilson loop, glueball Regge trajectory and stringy hadron masses in the Witten model of nonsupersymmetric, large-$N$ Yang-Mills theory. The classical string configurations corresponding to the above field theory objects are, respectively: open straight strings, folded closed spinning strings, and strings orbiting in the internal part of the supergravity background. For the rectangular Wilson loop we show that besides the standard Lüscher term, string corrections provide a rescaling of the field theory string tension. The one-loop corrections to the linear glueball Regge trajectories render them nonlinear with a positive intercept, as in the experimental soft Pomeron trajectory. Strings orbiting in the internal space predict a spectrum of hadroniclike states charged under global flavor symmetries which falls in the same universality class of other confining models.

We study four-dimensional low energy effective actions for conifold transitions of Calabi-Yau spaces in the context of IIB supergravity. The actions are constructed by examining the mass of D3-branes wrapped on collapsing/expanding three-cycles. We then study the cosmology of the conifold transition, including consequences for moduli stabilization, taking into account the effect of the additional states which become light at the transition. We find, the degree to which the additional states are excited is essential for whether the transition is dynamically realized.

In this paper, we use the strong field limit approach to investigate the gravitational lensing properties of braneworld black holes. Applying this method to the supermassive black hole at the center of our galaxy, the lensing observables for some candidate braneworld black hole metrics are compared with those for the standard Schwarzschild case. It is found that braneworld black holes could have significantly different observational signatures to the Schwarzschild black hole.

We present a general construction of initial data for Einstein’s equations containing an arbitrary number of black holes, each of which is instantaneously in equilibrium. Each black hole is taken to be a marginally trapped surface and plays the role of the inner boundary of the Cauchy surface. The black hole is taken to be instantaneously isolated if its outgoing null rays are shear-free. Starting from the choice of a conformal metric and the freely specifiable part of the extrinsic curvature in the bulk, we give a prescription for choosing the shape of the inner boundaries and the boundary conditions that must be imposed there. We show that with these choices, the resulting nonlinear elliptic system always admits solutions.

We construct numerically new axially symmetric solutions of SU(2) Yang-Mills-Higgs theory in $(3+1)$ anti-de Sitter spacetime. Two types of finite energy, regular configurations are considered: multimonopole solutions with magnetic charge $n>1$ and monopole-antimonopole pairs with zero net magnetic charge. A somewhat detailed analysis of the boundary conditions for axially symmetric solutions is presented. The properties of these solutions are investigated, with a view to compare with those on a flat spacetime background. The basic properties of the gravitating generalizations of these configurations are also discussed.

We compute the vacuum polarization associated with quantum massless fields around stars with spherical symmetry. The nonlocal contribution to the vacuum polarization is dominant in the weak field limit and induces quantum corrections to the static exterior metric that depend on the inner structure of the star. It also violates the null energy conditions. We argue that similar results also hold in the low energy limit of quantum gravity. Previous calculations of the vacuum polarization in spherically symmetric spacetimes, based on local approximations, are not adequate for Newtonian stars.