The Monte-Carlo method is applied to the Polyakov-loop extended Nambu–Jona-Lasinio model. This leads beyond the saddle-point approximation in a mean-field calculation and introduces fluctuations around the mean fields. We study the impact of fluctuations on the thermodynamics of the model, both in the case of pure gauge theory and including two quark flavors. In the two-flavor case, we calculate the second-order Taylor expansion coefficients of the thermodynamic grand canonical partition function with respect to the quark chemical potential and present a comparison with extrapolations from lattice QCD. We show that the introduction of fluctuations produces only small changes in the behavior of the order parameters for chiral symmetry restoration and the deconfinement transition. On the other hand, we find that fluctuations are necessary in order to reproduce lattice data for the flavor nondiagonal quark susceptibilities. Of particular importance are pion fields, the contribution of which is strictly zero in the saddle point approximation.

Significant progress in understanding quarkonium production requires improved polarization measurements, fully considering the intrinsic multidimensionality of the problem. We propose a frame-invariant formalism which minimizes the dependence of the measured result on the experimental acceptance, facilitates the comparison with theoretical calculations, and provides a much needed control over systematic effects due to detector limitations and analysis biases. This formalism is a direct and generic consequence of the rotational invariance of the dilepton decay distribution and is independent of any assumptions specific to particular models of quarkonium production.

We study holographic superconductors in $3+1$ dimensions away from the probe limit, i.e. taking backreaction of the space-time into account. We consider the case of pure Einstein and Gauss-Bonnet gravity, respectively. Similar to the probe limit we observe that the critical temperature at which condensation sets in decreases with increasing Gauss-Bonnet coupling. The decrease is however stronger when taking backreaction of the space-time into account. We observe that the critical temperature becomes very small, but stays positive for all values of the Gauss-Bonnet coupling no matter how strong the backreaction of the space-time is.

We extend the analysis of Alday and Maldacena for obtaining gluon scattering amplitudes at strong coupling to include external massive quark states. Our quarks are actually the $\mathcal{N}=2$ hypermultiplets which arise when $D7$-brane probes are included in the ${\mathrm{AdS}}_5\times S^5$ geometry. We work in the quenched approximation, treating the $\mathcal{N}=2$ matter multiplets as external sources coupled to the $\mathcal{N}=4$ supersymmetric Yang-Mills fields. We first derive appropriate massive-particle boundary conditions for the string scattering world sheets. We then find an exact world sheet which corresponds to the scattering of two massive quarks and two massless gluons and extract from this the associated scattering amplitude. We also find the world sheet and amplitude for the scattering of four massive quarks. Our world sheet solutions reduce to the four massless gluon solution of Alday and Maldacena in the limit of zero quark mass. The amplitudes we compute can also be interpreted in terms of 2-2 scattering involving gluons and massive $W$ bosons.

A collision of orbifold planes in 11 dimensions has been proposed as an explanation of the hot big bang [1,2,10]. When the two planes are close to each other, the winding membranes become the lightest modes of the theory, and can be effectively described in terms of fundamental strings in a ten-dimensional background. Near the brane collision, the 11-dimensional metric is a Euclidean space times a $1+1$-dimensional Milne universe. However, one may expect small perturbations to lead into a more general Kasner background. In this paper we extend the previous classical analysis of winding membranes to Kasner backgrounds, and using the Hamiltonian equations, solve for the wave function of loops with circular symmetry. The evolution across the singularity is regular, and explained in terms of the excitement of higher oscillation modes. We also show there is finite particle production and unitarity is preserved.

We investigate the dynamical 3-form flux compactifications and their implications for cosmology in our brane world in the six-dimensional Nishino-Salam-Sezgin model, which is usually referred to as the Salam-Sezgin model. We take the background of the 3-form field acting on the internal space and timelike dimensions without the $U(1)$ gauge field strength. The first class of solutions we discuss is the dynamical generalization of the static solutions obtained recently. In this class, we find that the time evolution is restricted only in the azimuthal dimension of the internal space and not in the ordinary three-dimensional one, which does not give a cosmological evolution. The second class of solutions is obtained by exchanging the roles of the radial coordinate and the time coordinate from the assumptions in the first class. At the center of the internal space, there is a conical singularity which may be interpreted as our 3-brane world, but it is difficult to realize a warped structure in the direction of the ordinary 3-space. Except for the oscillating solutions, a dynamical evolution leads to expanding or contracting ordinary 3-space, depending on the choice of time direction. Furthermore, in the expanding solutions, there are decelerating and accelerating ones: In the latter solution, the evolution is sustained for a finite proper time and the scale factor of the 3-space diverges.

We study 5D gauge symmetries in the Randall-Sundrum geometry that are hidden from the standard model through either small 5D gauge coupling, or through vanishing quantum numbers for the standard model fields. Geometric warping of 5D gravity creates a TeV-scale bridge from the standard model to the hidden sector gauge fields. We apply these concepts to a revival of the electroweak axion model, in which the dynamics of Peccei-Quinn symmetry breaking occur at the TeV scale.

Recent work on holographic superconductivity and gravitational duals of systems with nonrelativistic conformal symmetry have made use of consistent truncations of $D=10$ and $D=11$ supergravity retaining some massive modes in the Kaluza-Klein tower. In this paper we focus on reductions of type-IIB supergravity to five dimensions on a Sasaki-Einstein manifold, and extend these previous truncations to encompass the entire bosonic sector of gauged $D=5$, $\mathcal{N}=2$ supergravity coupled to massive multiplets up to the second Kaluza-Klein level. We conjecture that a necessary condition for the consistency of massive truncations is to only retain the lowest modes in the massive trajectories of the Kaluza-Klein mode decomposition of the original fields. This is an extension of the well-known result that consistent truncations may be obtained by restricting to the singlet sector of the internal symmetry group.

A warm inflationary universe model in loop quantum cosmology is studied. In general we discuss the condition of inflation in this framework. By using a chaotic potential, $V(\varphi )\propto {\varphi }^2$, we develop a model where the dissipation coefficient $\Gamma ={\Gamma }_0=\mathrm{\text{constant}}$. We use recent astronomical observations for constraining the parameters appearing in our model.

The Wilkinson Microwave Anisotropy Probe (WMAP) experiment has detected reionization at the $5.5\sigma$ level and has reported a mean optical depth of $0.088\pm 0.015$. A powerful probe of reionization is the large-angle $EE$ polarization power spectrum, which is now (since the first five years of data from WMAP) cosmic variance limited for $2\le l\le 6$. Here we consider partial reionization caused by weakly interacting massive particle dark matter annihilation, and calculate the expected polarization power spectrum. We compare the dark matter models with a standard two-step reionization theory, and examine whether the models may be distinguished using current, and future cosmic microwave background (CMB) observations. We consider dark matter annihilation at intermediate redshifts ($z<60$) due to halos, as well as annihilation at higher redshifts due to free particles. In order to study the effect of high redshift dark matter annihilation on CMB power spectra, it is essential to include the contribution of residual electrons (left over from recombination) to the ionization history. Dark matter halos at redshifts $z<60$ influence the low multipoles $l<20$ in the $EE$ power spectrum, while the annihilation of free particle dark matter at high redshifts $z>100$ mainly affects multipoles $l>10$.

We study the correlation between spin-independent and spin-dependent scattering in the context of minimal supersymmetric standard model neutralino dark matter for both thermal and nonthermal histories. We explore the generality of this relationship with reference to other models. We discuss why either fine-tuning or numerical coincidences are necessary for the correlation to break down. We derive upper bounds on spin-dependent scattering mediated by a $Z^0$ boson.

We construct a new, simple phenomenological model along the lines of AdS/QCD. The essential new ingredient is the brane-antibrane effective action including the open string tachyon proposed by Sen [Phys. Rev. D 68, 066008 (2003).]. Chiral symmetry breaking happens because of tachyon dynamics. We fit a large number of low-spin meson masses at the 10%–15% level. The only free parameters involved in the fits correspond to the overall QCD scale and the quark masses. Several aspects of previous models are qualitatively improved.

Although the sneutrino is a viable next-to-lightest supersymmetric particle candidate with gravitino lightest supersymmetric particle, spectra of this type occupy a part of supersymmetry parameter space in which collider signatures are poorly studied. In this paper we will extend previous work on this topic to include sneutrino next-to-lightest supersymmetric particle spectra with nonminimal phenomenology. Generally, these spectra exhibit very leptophilic behavior, which can be easily observed at the LHC. We show that a variety of such spectra can be analyzed with similar techniques, leading in each case to very suggestive evidence for complicated decay chains that end in sneutrinos. Amongst the variations considered, we find a simple class of spectra that produce signals with strong electron-muon asymmetries. These signals could naively be interpreted as evidence for lepton flavor violation, but can occur even with flavor-blind supersymmetry.

A search for the neutrinoless, lepton-flavor violating decay of the $\tau$ lepton into three charged leptons has been performed using an integrated luminosity of $468{\mathrm{fb}}^{-1}$ collected with the BABAR detector at the PEP-II collider. In all six decay modes considered, the numbers of events found in data are compatible with the background expectations. Upper limits on the branching fractions are set in the range $(1.8–3.3)\times {10}^{-8}$ at 90% confidence level.

We reexamine the bending of light issue associated with the metric of the static, spherically symmetric solution of Weyl gravity discovered by Mannheim and Kazanas (1989). To this end we employ the procedure used recently by Rindler and Ishak to obtain the bending angle of light by a centrally concentrated spherically symmetric matter distribution in a Schwarzschild–de Sitter background. In earlier studies the term $\gamma r$ in the metric led to the paradoxical result of a bending angle proportional to the photon impact parameter, when using the usual formalism appropriate to asymptotically flat space-times. However, employing the approach of light bending of Rindler and Ishak we show that the effects of this term are in fact insignificant, with the discrepancy between the two procedures attributed to the definition of the bending angle between the asymptotically flat and nonflat spaces.

We perform a full perturbative stability analysis of the 6D cascading gravity model in the presence of 3-brane tension. We demonstrate that for sufficiently large tension on the (flat) 3-brane, there are no ghosts at the perturbative level, consistent with results that had previously only been obtained in a specific 5D decoupling limit. These results establish the cascading gravity framework as a consistent infrared modification of gravity.

An alternative expression for the length operator in loop quantum gravity is presented. The operator is background independent, symmetric, positive semidefinite, and well defined on the kinematical Hilbert space. The expression for the regularized length operator can moreover be understood both from a simple geometrical perspective as the average of a formula relating the length to area, volume and flux operators, and also consistently as the result of direct substitution of the densitized triad operator with the functional derivative operator into the regularized expression of the length. Both these derivations are discussed, and the origin of an undetermined overall factor in each case is also elucidated.

Building on earlier work on football-shaped extra dimensions, we construct a compact codimension-two braneworld with precisely one brane. The two extra dimensions topologically represent a 2-torus which is stabilized by a bulk cosmological constant and magnetic flux. The torus has positive constant curvature almost everywhere, except for a single conical singularity at the location of the brane. In contradistinction to the football-shaped case, there is no fine-tuning required for the brane tension. We also present some plausibility arguments why the model should not suffer from serious stability issues.

The covariant canonical expression for the conserved charges, proposed by Nester, is tested on several solutions in three-dimensional gravity with or without torsion and topologically massive gravity. In each of these cases, the calculated values of energy momentum and angular momentum are found to satisfy the first law of black hole thermodynamics.