We determine the partition function of $\frac{1}{16}\mathrm{BPS}$ operators in $\mathcal{N}=4$ super Yang-Mills (SYM) at weak coupling at the one-loop level in the planar limit. This partition function is significantly different from the one computed at zero coupling. We find that it coincides precisely with the partition function of a gas of $\frac{1}{16}\mathrm{BPS}$ supergravitons in ${\mathrm{AdS}}_5\times S^5$.

The variational approach to the Hamilton formulation of Yang-Mills theory in Coulomb gauge developed by the present authors previously is applied to Yang-Mills theory in $2+1$ dimensions and is confronted with the existing lattice data. We show that the resulting Dyson-Schwinger equations (DSE) yield consistent solutions in $2+1$ dimensions only for infrared divergent ghost form factor and gluon energy. The obtained numerical solutions of the DSE reproduce the analytic infrared results and are in satisfactory agreement with the existing lattice date in the whole momentum range.

We investigate the structure of protoneutron stars (PNS) formed by hadronic and quark matter in $\beta$-equilibrium described by appropriate equations of state (EOS). For the hadronic matter, we use a finite temperature EOS based on the Brueckner-Bethe-Goldstone many-body theory, with realistic two- and three-body forces. For the quark sector, we employ the Nambu–Jona-Lasinio model. We find that the allowed maximum masses are comprised in a narrow range around 1.8 solar masses, with a slight dependence on the temperature. Metastable hybrid protoneutron stars are not found.

We consider a modified action functional with a nonminimum coupling between the scalar curvature and the matter Lagrangian, and study its consequences on stellar equilibrium. Particular attention is paid to the validity of the Newtonian regime, and on the boundary and exterior matching conditions, as well as on the redefinition of the metric components. Comparison with solar observables is achieved through numerical analysis, and constraints on the nonminimum coupling are discussed.

We discuss observational consequences of a class of cosmological models characterized by the dilution of pressureless matter attenuated with respect to the usual $a^{-3}$ scaling due to the decay of vacuum energy. We carry out a joint statistical analysis of observational data from the new gold sample of 182 SNe Ia, recent estimates of the cosmic microwave background shift parameter, and baryon acoustic oscillations measurements from the SDSS to show that such models favor the decay of vacuum only into the dark matter sector, and that the separately conserved baryons cannot be neglected. In order to explore ways to more fundamentally motivate these models, we also derive a coupled scalar field version for this general class of vacuum decay scenarios.

The thawing quintessence model with a nearly flat potential provides a natural mechanism to produce an equation of state parameter, $w$, close to $-1$ today. We examine the behavior of such models for the case in which the potential satisfies the slow-roll conditions: $[(1/V)(dV/d\varphi ){]}^2\ll 1$ and $(1/V)(d^{2}V/d{\varphi }^2)\ll 1$, and we derive the analog of the slow-roll approximation for the case in which both matter and a scalar field contribute to the density. We show that in this limit, all such models converge to a unique relation between $1+w$, ${\Omega }_{\varphi }$, and the initial value of $(1/V)(dV/d\varphi )$. We derive this relation and use it to determine the corresponding expression for $w(a)$, which depends only on the presentday values for $w$ and ${\Omega }_{\varphi }$. For a variety of potentials, our limiting expression for $w(a)$ is typically accurate to within $\delta w\lesssim 0.005$ for $w<-0.9$. For redshift $z\lesssim 1$, $w(a)$ is well fit by the Chevallier-Polarski-Linder parametrization, in which $w(a)$ is a linear function of $a$.

Doubly charged Higgs bosons ($H^{\pm \pm }$) are a distinctive signature of the Higgs triplet model of neutrino mass generation. If $H^{\pm \pm }$ is relatively light ($m_{H^{\pm \pm }}<400\mathrm{GeV}$), it will be produced copiously at the LHC, which could enable precise measurements of the branching ratios of the decay channels $H^{\pm \pm }\to l_i^{\pm }{l}_j^{\pm }$. Such branching ratios are determined solely by the neutrino mass matrix which allows the model to be tested at the LHC. We quantify the dependence of the leptonic branching ratios on the absolute neutrino mass and Majorana phases, and present the permitted values for the channels $e^{\pm }{e}^{\pm }$, $e^{\pm }{\mu }^{\pm }$, and ${\mu }^{\pm }{\mu }^{\pm }$. It is shown that precise measurements of these three branching ratios are sufficient to extract information on the neutrino mass spectrum and probe the presence of $CP$ violation from Majorana phases.

Extrapolations of soft scalar mass parameters in supersymmetric theories can be used to explore elements of the physics scenario near the grand unification scale. We investigate the potential of this method in the lepton sector of SO(10) which incorporates right-handed neutrino superfields. The method is exemplified in two models by exploring limits on the precision that can be expected from coherent LHC and $e^{+}{e}^{-}$ collider analyses in the reconstruction of the fundamental scalar mass parameters at the unification scale and of the D-terms related to the breaking of grand unification symmetries. In addition, the mass of the third-generation right-handed neutrino can be estimated in seesaw scenarios. Even though the models are simplified and not intended to account for all aspects of a final comprehensive SO(10) theory, they provide nevertheless a valid base for identifying essential elements that can be inferred on the fundamental high-scale theory from high-energy experiments.

We study the properties of configurations from which P-vortices on one hand or Abelian monopoles on the other hand have been removed. We find that the zero modes and the band of nonzero modes close to zero disappear from the spectrum of the overlap Dirac operator, confirming the absence of topological charge and quark condensate. The different behavior of the modified ensembles under smearing compared to the unmodified Monte Carlo ensemble corroborates these findings. The gluonic topological susceptibility rapidly approaches zero in accordance with $Q_{\mathrm{index}}=0$. The remaining (ultraviolet) monopoles without vortices and—to a less extent—the remaining vortices without monopoles are unstable under smearing whereas smearing of the unmodified Monte Carlo ensemble affects the monopoles and vortices only by smoothing, reducing the density only slightly.

New high statistics Belle data on the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ reaction cross section measured in the range of pion-pair invariant masses $\sqrt{s}$ between 0.8 GeV and 1.5 GeV are analyzed to clarify the current situation around the $\sigma (600)$, $f_0(980)$, and $f_2(1270)$ resonances in $\gamma \gamma$ collisions. The present analysis shows that the direct coupling constants of the $\sigma (600)$ and $f_0(980)$ resonances to $\gamma \gamma$ are small, and the $\sigma (600)\to \gamma \gamma$ and $f_0(980)\to \gamma \gamma$ decays are four-quark transitions caused by the ${\pi }^{+}{\pi }^{-}$ and $K^{+}{K}^{-}$ loop mechanisms, respectively. The chiral shielding of the $\sigma (600)$ resonance takes place in the reactions $\gamma \gamma \to \pi \pi$ as well as in $\pi \pi$ scattering. Some results of a simultaneous description of the $\gamma \gamma \to {\pi }^{+}{\pi }^{-}$ and $\gamma \gamma \to {\pi }^0{\pi }^0$ Belle data are also presented. In particular, the following tentative estimate of the $f_2(1270)\to \gamma \gamma$ decay width is obtained: ${\Gamma }_{f_2\to \gamma \gamma }(m_{f_2}^2)\approx 3.68\mathrm{keV}$.

We study the Collins effect in the azimuthal asymmetric distribution of hadrons inside a high energy jet in the single-transverse polarized proton-proton scattering. From the detailed analysis of one-gluon and two-gluon exchange diagrams contributions in a particular model, the Collins function is found the same as that in the semi-inclusive deep inelastic scattering and $e^{+}{e}^{-}$ annihilations. The eikonal propagators in these diagrams do not contribute to the phase needed for the Collins-type single-spin asymmetry, and the universality is derived as a result of the Ward identity. We argue that this conclusion depends on the momentum flow of the exchanged gluon and the kinematic constraints in the fragmentation process.

We study how the charge neutrality affects the phase structure of the three-flavor Polyakov-loop Nambu–Jona-Lasinio (PNJL) model. We point out that, within the conventional PNJL model at finite density, the color neutrality is missing because the Wilson line serves as an external colored field coupled to dynamical quarks. In this paper we heuristically assume that the model may still be applicable. To get color neutrality, one has then to allow nonvanishing color chemical potentials. We study how the quark matter phase diagram in $(T,m_s^2/\mu )$-plane is affected by imposing neutrality and by including the Polyakov-loop dynamics. Although these two effects are correlated in a nonlinear way, the impact of the Polyakov loop turns out to be significant in the $T$ direction, while imposing neutrality brings a remarkable effect in the $m_s^2/\mu$ direction. In particular, we find a novel unlocking transition, when the temperature is increased, even in the chiral $SU(3)$ limit. We clarify how and why this is possible once the dynamics of the colored Polyakov loop is taken into account. Also we succeed in giving an analytic expression for $T_c$ for the transition from two-flavor pairing (2SC) to unpaired quark matter in the presence of the Polyakov loop.

We investigate how the baryon asymmetry of our Universe via leptogenesis can be achieved within the framework of the seesaw model with Fritzsch-type lepton mass matrices proposed by Fukugita et al. We study the cases with $CP$-violating phases in charged-lepton Yukawa matrix, however, with and without Dirac neutrino Yukawa phases. We consider both flavor-independent and flavor-dependent leptogenesis, and demonstrate how they lead to different amounts of lepton asymmetries in detail. In particular, it is shown that flavor-dependent leptogenesis in this model can be achieved only for very tiny or zero values of $CP$ phases in Dirac neutrino Yukawa matrix at the grand unified theory scale. In addition to the $CP$ phases, for successful leptogenesis in the model it is required that the degeneracy of the heavy Majorana neutrino mass spectrum should be broken and we also show that the breakdown of the degeneracy can be radiatively induced.

We present for the first time a measurement of the weak phase $2\beta +\gamma$ obtained from a time-dependent Dalitz plot analysis of $B^0\to D^{\mp }{K}^0{\pi }^{\pm }$ decays. Using a sample of approximately $347\times {10}^6$ $B\overline{B}$ pairs collected by the BABAR detector at the PEP-II asymmetric-energy storage rings and assuming the ratio $r$ of the $b\to u$ and $b\to c$ decay amplitudes to be 0.3, we obtain $2\beta +\gamma =(83\pm 53\pm 20)°$ and the equivalent solution at $+180°$. The magnitudes and phases for the resonances associated with the $b\to c$ transitions are also extracted from the fit.

We consider the entanglement entropy for a subsystem in $d+1$ dimensional $SU(N)$ lattice gauge theory. The $1+1$ gauge theory is treated exactly and shows trivial behavior. Gauge theories in higher dimensions are treated within Migdal-Kadanoff approximation. We consider the gauge theory in the confinement phase. We demonstrate the existence of a nonanalytical change from the short distance to long distance form in the entanglement entropy in such systems ($d>2$) reminiscent of phase transition. The transition is manifested in nontrivial change in the renormalization group flow of character expansion coefficients defining the partition function.

It is usually assumed that dark matter is produced during the radiation-dominated era. There is, however, no direct evidence for radiation domination prior to big-bang nucleosynthesis. Two nonstandard thermal histories are considered. In one, the low-temperature-reheating scenario, radiation domination begins as late as $\sim 1\mathrm{MeV}$, and is preceded by significant entropy generation. Thermal axion relic abundances are then suppressed, and cosmological limits to axions are loosened. For reheating temperatures $T_{\mathrm{rh}}\lesssim 35\mathrm{MeV}$, the large-scale structure limit to the axion mass is lifted. The remaining constraint from the total density of matter is significantly relaxed. Constraints are also relaxed for higher reheating temperatures. In a kination scenario, a more modest change to cosmological axion constraints is obtained. Future possible constraints to axions and low-temperature reheating from the helium abundance and next-generation large-scale-structure surveys are discussed.

We consider a ($1+1$) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe—on the order of 50%—is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences.

Using techniques from singular perturbation theory, we explicitly calculate the cosmological evolution in a class of modified gravity models. By considering both the CDTT and modified CDTT (mCDTT) models, which aims to explain the current acceleration of the universe with a modification of gravity, we show that Einstein evolution can be recovered for most of cosmic history in at least one $f(R)$ model. We show that a standard epoch of matter domination can be obtained in the mCDTT model, providing a sufficiently long epoch to satisfy observations. We note that the additional inverse term will not significantly alter standard evolution until today and that the solution lies well within present constraints from big bang nucleosynthesis. For the CDTT model, we analyze the “recent radiation epoch” behavior ($a\propto t^{1/2}$) found by previous authors. We finally generalize our findings to the class of inverse power-law models. Even in this class of models, we expect a standard cosmological evolution, with a sufficient matter domination era, although the sign of the additional term is crucial.

Future multifrequency microwave background experiments with arcminute resolution and micro-Kelvin temperature sensitivity will be able to detect the kinetic Sunyaev-Zeldovich effect, providing a way to measure radial peculiar velocities of massive galaxy clusters. We show that cluster peculiar velocities have the potential to constrain several dark energy parameters. We compare three velocity statistics (the distribution of radial velocities, the mean pairwise streaming velocity, and the velocity correlation function) and analyze the relative merits of these statistics in constraining dark energy parameters. Of the three statistics, mean pairwise streaming velocity provides constraints that are least sensitive to velocity errors: the constraints on parameters degrade only by a factor of 2 when the random error is increased from 100 to $500\mathrm{km}/\mathrm{s}$. We also compare cluster velocities with other dark energy probes proposed in the Dark Energy Task Force report. For cluster velocity measurements with realistic priors, the eventual constraints on the dark energy density, the dark energy equation of state and its evolution are comparable to constraints from supernovae measurements, and better than cluster counts and baryon acoustic oscillations; adding velocity to other dark energy probes improves constraints on the figure of merit by more than a factor of 2. For upcoming Sunyaev-Zeldovich galaxy cluster surveys, even velocity measurements with errors as large as $1000\mathrm{km}/\mathrm{s}$ will substantially improve the cosmological constraints compared to using the cluster number density alone.

We estimate the probability of detecting a gravitational wave signal from coalescing compact binaries in simulated data from a ground-based interferometer detector of gravitational radiation using Bayesian model selection. The simulated wave form of the chirp signal is assumed to be a spinless post-Newtonian (PN) wave form of a given expansion order, while the searching template is assumed to be either of the same post-Newtonian family as the simulated signal or one level below its post-Newtonian expansion order. Within the Bayesian framework, and by applying a reversible jump Markov Chain Monte Carlo simulation algorithm, we compare PN1.5 vs PN2.0 and PN3.0 vs PN3.5 wave forms by deriving the detection probabilities, the statistical uncertainties due to noise as a function of the signal-to-noise ratio, and the posterior distributions of the parameters. Our analysis indicates that the detection probabilities are not compromised when simplified models are used for the comparison, while the accuracies in the determination of the parameters characterizing these signals can be significantly worsened, no matter what the considered post-Newtonian order expansion comparison is.