In this paper we study the renormalization of the Schwinger-Dyson equations that arise in the auxiliary field formulation of the O($N$) ${\varphi }^4$ field theory. The auxiliary field formulation allows a simple interpretation of the large-$N$ expansion as a loop expansion of the generating functional in the auxiliary field $\chi$, once the effective action is obtained by integrating over the $\varphi$ fields. Our all orders result is then used to obtain finite renormalized Schwinger-Dyson (SD) equations based on truncation expansions which utilize the two-particle irreducible (2-PI) generating function formalism. We first do an all orders renormalization of the two- and three-point function equations in the vacuum sector. This result is then used to obtain explicitly finite and renormalization constant independent self-consistent SD equations valid to order $1/N$, in both $2+1$ and $3+1$ dimensions. We compare the results for the real and imaginary parts of the renormalized Green’s functions with the related sunset approximation to the 2-PI equations discussed by Van Hees and Knoll, and comment on the importance of the Landau pole effect.

A numerical and analytic treatment is presented here of the evolution of initial data of the kind that was conjectured by Hertog, Horowitz and Maeda to lead to a violation of cosmic censorship. That initial data is essentially a thick domain wall connecting two regions of anti de Sitter space. The evolution results in no violation of cosmic censorship, but rather the formation of a small black hole.

The exact five-dimensional charged black hole solution in Lovelock gravity coupled to Born-Infeld electrodynamics is presented. This solution interpolates between the Hoffmann black hole for the Einstein-Born-Infeld theory and other solutions in the Lovelock theory previously studied in the literature. It is shown how the conical singularity of the metric around the origin can be removed by a proper choice of the black hole parameters. The differences existing with the Reissner-Nordström black holes are discussed. In particular, we show the existence of charged black holes with a unique horizon.

We examine the generation and evolution of perturbations in a universe dominated by a fluid with stiff equation of state $p=\rho$. The recently proposed holographic universe is an example of such a model. We compute the spectrum of scalar and tensor perturbations, without relying on a microphysical description of the $p=\rho$ fluid. The spectrum is scale invariant deep inside the Hubble horizon. In contrast, infrared perturbations that enter the Hubble horizon during the stiff fluid dominated (holographic) phase yield oscillatory and logarithmic terms in the power spectrum. We show that vector perturbations grow during the stiff fluid dominated epoch and may result in a turbulent and anisotropic universe at the end of the holographic phase. Therefore, the required period of inflation following the holographic phase cannot be much shorter than that required in standard inflationary models.

We examine some cosmological consequences of gravity coupling with different strength to fermions and bosons. We show that this leads to a different perturbation of the standard picture of primordial nucleosynthesis than the addition of extra neutrino types or overall scaling of the value of $G$. Observed abundances of deuterium and ${}^4\mathrm{H}\mathrm{e}$ place bounds on the ratio of the bosonic gravitational constant ($G_B$) to the fermionic gravitational constant ($G_F$) of $0.45<G_B/G_F<0.92$ at $1\sigma$ and $0.33<G_B/G_F<1.10$ at $2\sigma$. A value of $G_B<G_F$ can reconcile the current “tension” between the abundances of deuterium and ${}^4\mathrm{H}\mathrm{e}$ predicted by primordial nucleosynthesis. We comment briefly on other cosmological effects.

We study constraints on a number of patch inflationary models in noncommutative spacetime using a compilation of recent high-precision observational data. In particular, the four-dimensional general relativistic (GR) case, the Randall-Sundrum (RS), and the Gauss-Bonnet brane world scenarios are investigated by extending previous commutative analyses to the infrared limit of a maximally symmetric realization of the stringy uncertainty principle. The effect of spacetime noncommutativity modifies the standard consistency relation between the tensor spectral index and the tensor-to-scalar ratio. We perform likelihood analyses in terms of inflationary observables using new consistency relations and confront them with large-field inflationary models with potential $V\propto {\phi }^p$ in two classes of noncommutative scenarios. We find a number of interesting results: (i) the quartic potential ($p=4$) is rescued from marginal rejection in the class 2 GR case, and (ii) steep inflation driven by an exponential potential ($p\to \infty$) is allowed in the class 1 RS case. Spacetime noncommutativity can lead to blue-tilted scalar and tensor spectra even for monomial potentials, thus opening up a possibility to explain the loss of power observed in cosmic microwave background anisotropies. We also explore patch inflation with a Dirac-Born-Infeld tachyon field and explicitly show that the associated likelihood analysis is equivalent to the one in the ordinary scalar field case by using horizon-flow parameters. It turns out that tachyon inflation is compatible with observations in all patch cosmologies even for large $p$.

We study some consequences of noncommutativity to homogeneous cosmologies by introducing a deformation of the commutation relation between the minisuperspace variables. The investigation is carried out for the Kantowski-Sachs model by means of a comparative study of the universe evolution in four different scenarios: the classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative. The comparison is rendered transparent by the use of the Bohmian formalism of quantum trajectories. As a result of our analysis, we found that noncommutativity can modify significantly the universe evolution, but cannot alter its singular behavior in the classical context. Quantum effects, on the other hand, can originate nonsingular periodic universes in both commutative and noncommutative cases. The quantum noncommutative model is shown to present interesting properties, as the capability to give rise to nontrivial dynamics in situations where its commutative counterpart is necessarily static.

It is argued that in the case of a (four-dimensional) smooth transition across a (dilaton-driven) curvature bounce growing vector fluctuations evolve continuously into decaying solutions at later times in the post-bounce epoch. Analytical examples of this observation are given. In the case of multidimensional bouncing models the situation is different, since the system of differential equations describing the vector modes of the geometry has a richer structure. The amplification of the vector modes of the geometry is specifically investigated in a regular five-dimensional bouncing curvature model where scale factors of the external and internal manifolds evolve at a dual rate. Vector fluctuations, in this case, can be copiously produced and are continuous across the bounce. The relevance of these results is critically illustrated.

High energy particle showers produce coherent Cherenkov radio emission in dense, radio-transparent media such as cold ice. Using PYTHIA and GEANT simulation tools, we make a comparative study among electromagnetic (EM) and hadronic showers initiated by single particles and neutrino showers initiated by multiple particles produced at the neutrino-nucleon event vertex. We include all the physics processes and do a complete 3D simulation up to 100 TeV for all showers and to 1 PeV for electron- and neutrino-induced showers. We calculate the radio pulses for energies between 100 GeV and 1 PeV and find hadron showers, and consequently neutrino showers, are not as efficient below 1 PeV at producing radio pulses as the electromagnetic showers. The agreement improves as energy increases, however, and by a PeV and above the difference disappears. By looking at the 3D structure of the showers in time, we show that the hadronic showers are not as compact as the EM showers and hence the radiation is not as coherent as EM shower emission at the same frequency. We show that the ratio of emitted pulse strength to shower tracklength is a function only of a single, coherence parameter, independent of species and energy of initiating particle.

The measurements of the angular power spectrum of the Cosmic Microwave Background (CMB) anisotropy have proved crucial to the emergence of cosmology as a precision science in recent years. In this remarkable data rich period, the limitations to precision now arise from the inability to account for finer systematic effects in data analysis. The noncircularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. We present an analytic framework for studying the leading order effects of a noncircular beam on the CMB power spectrum estimation. We consider a noncircular beam of fixed shape but variable orientation. We compute the bias in the pseudo-$C_l$ power spectrum estimator and then construct an unbiased estimator using the bias matrix. The covariance matrix of the unbiased estimator is computed for smooth, noncircular beams. Quantitative results are shown for CMB maps made by a hypothetical experiment with a noncircular beam comparable to our fits to the Wilkinson Microwave Anisotropy Probe (WMAP) beam maps described in the appendix and uses a toy scan strategy. We find that significant effects on CMB power spectrum can arise due to noncircular beam on multipoles comparable to, and beyond, the inverse average beamwidth where the pseudo-$C_l$ approach may be the method of choice due to computational limitations of analyzing the large data sets from current and near future CMB experiments.

We investigate the possibility that dark energy is scaling with epochs. A phenomenological model is introduced whose energy density depends on the redshift $z$ in such a way that a smooth transition among the three dominant phases of the Universe evolution (radiation era, matter domination, asymptotic de Sitter state) is achieved. We use the Wilkinson Microwave Anisotropy Probe cosmic microwave background data and the luminosity distances of Type Ia Supernovae to test whether the model is in agreement with astrophysical observations.

We investigate phase structure of the $D(>4)$-dimensional gauged Nambu-Jona-Lasinio (NJL) model with $\delta (=D-4)$ extra dimensions compactified on TeV scale, based on the improved ladder Schwinger-Dyson (SD) equation in the bulk. We assume that the bulk (dimensionless) running gauge coupling in the SD equation for the $\mathrm{S}\mathrm{U}(N_c)$ gauge theory with $N_f$ massless flavors is given by the truncated Kaluza-Klein effective theory and hence has a nontrivial ultraviolet fixed point (UVFP), resulting in the walking coupling. We find the critical line in the parameter space of two couplings, the gauge coupling (value fixed at the UVFP) and the (dimensionless) four-fermion coupling, which is similar to that of the gauged NJL model with fixed (walking) gauge coupling in four dimensions. It is shown that in the presence of such walking gauge interactions the four-fermion interactions become nontrivial and renormalizable even in higher dimensions, similar to the four dimensional gauged NJL model. Such a renormalizability/nontriviality holds only in the restricted region of the critical line (“nontrivial window”) with the gauge coupling larger than a nonvanishing value (“marginal triviality” point), in contrast to the four dimensional case where such a renormalizability holds for all regions of the critical line except for the pure NJL point (without gauge coupling). In the nontrivial window the renormalized effective potential yields a nontrivial interaction which is conformal invariant. The existence of the nontrivial window implies “cutoff insensitivity” of the physics prediction in spite of the ultraviolet dominance of the dynamics. In the formal limit $D\to 4$, the nontrivial window shrinks to the pure NJL point but with a nontrivial condition which coincides with the known condition of the renormalizability/nontriviality of the four dimensional gauged NJL model, $\frac{9}{2}\frac{1}{N_c}<N_f-N_c<\frac{9}{2}{N}_c$.

We investigate the spectrum of the lightest states of $N=1$ Super Yang-Mills theory. We first study the spectrum using the recently extended Veneziano Yankielowicz theory containing also the glueball states besides the gluinoball ones. Using a simple Kähler term we show that within the effective Lagrangian approach one can accommodate either the possibility in which the glueballs are heavier or lighter than the gluinoball fields. We then provide an argument independent from the effective Lagrangian which allows, using information about ordinary QCD, to deduce that the lightest states in Super Yang-Mills theory are the gluinoballs. This helps constraining the Kähler term of the effective Lagrangian. Using this information and the effective Lagrangian we note that there is a small mixing among the gluinoball and glueball states.

The distinction between the rigid-rotor and Callan-Klebanov approaches to the quantization of SU(3) solitons is considered in the context of exotic baryons. A numerically tractable quantum mechanical analog system is introduced to test the reliability of the two quantization schemes. We find that in the equivalent of the large $N_c$ limit of QCD, the Callan-Klebanov approach agrees with a numerical solution of the quantum mechanical analog. Rigid-rotor quantization generally does not. The implications for exotic baryons are briefly discussed.

The neutrino masses are generated in grand unified theory (GUT) constrained supersymmetric model with R-parity violation. The neutrinos acquire masses via tree-level neutrino-neutralino mixing as well as via one-loop radiative corrections. The theoretical mass matrix is compared with the phenomenological one, which is reconstructed by using neutrino oscillation and neutrinoless double beta decay data. This procedure allows to obtain significantly stronger constraints on R-parity breaking parameters than those existing in the literature. The implication of normal and inverted neutrino mass hierarchy on the sneutrino expectation values, lepton-Higgs bilinear and trilinear R-parity breaking couplings is also discussed.

We study supersymmetric dark matter in the general flavor diagonal minimal supersymmetric standard model by means of an extensive random scan of its parameter space. We find that, in contrast with the standard minimal supergravity lore, the large majority of viable models features either a Higgsino or a winolike lightest neutralino, and yields a relic abundance well below the Wilkinson Microwave Anisotropy Probe (WMAP) bound. Among the models with neutralino relic density within the WMAP range, Higgsinolike neutralinos are still dominant, though a sizable fraction of binos is also present. In this latter case, coannihilations are shown to be essential in order to obtain the correct neutralino abundance. We then carry out a statistical analysis and a general discussion of neutralino dark matter direct detection and of indirect neutralino detection at neutrino telescopes and at antimatter search experiments. We point out that current data exclude only a marginal portion of the viable parameter space, and that models whose thermal relic abundance lies in the WMAP range will be significantly probed only at future direct detection experiments. Finally, we emphasize the importance of relic density enhancement mechanisms for indirect detection perspectives, in particular, at future antimatter search experiments.

We study the worldvolume dynamics of $1/2$-supersymmetric domain walls in $\mathcal{N}=1$ supersymmetric QCD with $N_f=N$ flavors, and exhibit an enhancement of supersymmetry for the reduced moduli space associated with broken flavor symmetries. We provide an explicit construction of the worldvolume superalgebra which corresponds to an $\mathcal{N}=2$ Kähler sigma model in $2+1\mathrm{D}$ deformed by a potential, given by the norm squared of a U(1) Killing vector, resulting from the flavor symmetries broken by unequal quark masses. This framework leads to a worldvolume description of novel two-wall-junction configurations, which are $1/4$-supersymmetric objects, but nonetheless preserve two supercharges when viewed as kinks on the wall worldvolume.

According to recent studies, Parton Distribution Functions (PDFs) and Generalized Parton Distributions (GPDs) can be evaluated in a Constituent Quark Model (CQM) scenario, considering the constituent quarks as composite objects. In here, a fully covariant model for a system of two particles, together with its non relativistic limit, are used to calculate PDFs and GPDs. The analysis permits to realize that by no means the effects of Relativity can be simulated taking into account the structure of the constituent particles, the two effects being independent and necessary for a proper description of available high energy data in terms of CQM.

In light of the large amount of new experimental data, we revisit the determination of $|V_{cb}|$ and $m_b$ from inclusive semileptonic and radiative $B$ decays. We study shape variables to order ${\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}^3/m_b^3$ and ${\alpha }_s^2{\beta }_0$, and include the order ${\alpha }_s{\Lambda }_{\mathrm{Q}\mathrm{C}\mathrm{D}}/m_b$ correction to the hadron mass spectrum in semileptonic decay, which improves the agreement with the data. We focus on the $1S$ and kinetic mass schemes for the $b$ quark, with and without expanding $m_b-m_c$ in heavy quark effective theory. We perform fits to all available data from BABAR, BELLE, CDF, CLEO, and DELPHI, discuss the theoretical uncertainties, and compare with earlier results. We find $|V_{cb}|=(41.4\pm 0.6\pm {0.1}_{{\tau }_B})\times {10}^{-3}$ and $m_b^{1S}=4.68\pm 0.03\mathrm{G}\mathrm{e}\mathrm{V}$, including our estimate of the theoretical uncertainty in the fit.

We study the evolution of flavor-singlet, light-cone amplitudes in the soft-collinear effective theory, and reproduce results previously obtained by a different approach. We apply our calculation to the color-singlet contribution to the photon endpoint in radiative ${\rm Y}$ decay. In a previous paper, we studied the color-singlet contributions to the endpoint, but neglected operator mixing, arguing that it should be a numerically small effect. Nevertheless the mixing needs to be included in a consistent calculation, and we do just that in this work. We find that the effects of mixing are indeed numerically small. This result combined with previous work on the color-octet contribution and the photon fragmentation contribution provides a consistent theoretical treatment of the photon spectrum in ${\rm Y}\to \gamma X$.