The effects of thermal fluctuations of the mass (horizon area) and electric charge, on the entropy of nonrotating charged macroscopic black holes, are analyzed using a grand canonical ensemble. Restricting to Gaussian fluctuations around equilibrium, and assuming a power-law type of relation between the black hole mass, charge and horizon area, characterized by two real positive indices, the grand canonical entropy is shown to acquire a logarithmic correction with a positive coefficient proportional to the sum of the indices. However, the root mean squared fluctuations of mass and charge relative to the mean values of these quantities turn out to be independent of the details of the assumed mass-area relation. We also comment on possible cancellation between log (area) corrections arising due to fixed area quantum spacetime fluctuations and that due to thermal fluctuations of the area and other quantities.

We analyze the implications of having a divergent speed of sound in $k$-essence cosmological models. We first study a known theory of that kind, for which the Lagrangian density depends linearly on the time derivative of the $k$-field. We show that when $k$-essence is the only source consistency requires that the potential of the $k$-field be of the inverse square form. Then, we review the known result that the corresponding power-law solutions can be mapped to power-law solutions of theories with no divergence in the speed of sound. After that, we argue that the requirement of a divergent sound speed at some point fixes uniquely the form of the Lagrangian to be exactly the one considered earlier and prove the asymptotic stability of the most interesting solutions belonging to the divergent theory. Then, we discuss the implications of having not just $k$-essence but also matter. This is interesting because introducing another component breaks the rigidity of the theory, and the form of the potential ceases to be unique as happened in the pure $k$-essence case. Finally, we show the finiteness of the effective sound speed under an appropiate definition.

It has recently been suggested that Planck scale physics may effect the evolution of cosmological fluctuations in the early stages of cosmological inflation in a nontrivial way, leading to an excited state for modes whose wavelength is super-Planck but sub-Hubble. In this case, the issue of how this excited state back-reacts on the background space-time arises. In fact, it has been suggested that such back-reaction effects may lead to tight constraints on the magnitude of possible deviations from the usual predictions of inflation. In this note we discuss some subtle aspects of this back-reaction issue and point out that rather than preventing inflation, the back-reaction of ultraviolet fluctuations may simply lead to a renormalization of the cosmological constant driving inflation.

The neutrino mixing matrix is expanded in powers of a small parameter $\lambda$ in tribimaximal mixing pattern. We also present some applications of this parametrization, such as to the expression of the Jarlskog parameter $J$. Comparing with other parametrizations (such as the parametrization in bimaximal mixing pattern), this parametrization converges more quickly, but is of less symmetry.

We derive a set of symmetry relations for the three-neutrino mixing angles, including the Mikheyev-Smirnov-Wolfenstein (MSW) matter effect. Though interesting in their own right, these relations are used to choose the physical region of the mixing angles such that oscillations are parametrized completely and uniquely. We propose that the preferred way of setting the bounds on the mixing angles should be ${\theta }_{12}\in [0,\pi /2]$, ${\theta }_{13}\in [-\pi /2,\pi /2]$, ${\theta }_{23}\in [0,\pi /2]$, and $\delta \in [0,\pi )$. No CP violation then results simply from setting $\delta =0$. In the presence of the MSW effect, this choice of bounds is a new result. Since the size of the asymmetry about ${\theta }_{13}=0$ is dependent on the details of the data analysis and is a part of the results of the analysis, we argue that the negative values of ${\theta }_{13}$ should not be ignored.

We recently showed that warped extra-dimensional models with bulk custodial symmetry and few TeV Kaluza-Klein (KK) masses lead to striking signals at $B$ factories. In this paper, using a spurion analysis, we systematically study the flavor structure of models that belong to the above class. In particular we find that the profiles of the zero modes, which are similar in all these models, essentially control the underlying flavor structure. This implies that our results are robust and model independent in this class of models. We discuss in detail the origin of the signals in $B$ physics. We also briefly study other new physics signatures that arise in rare $K$ decays ($K\to \pi \nu \nu$), in rare top decays [$t\to c\gamma (Z,\mathrm{\text{gluon}})$], and the possibility of $CP$ asymmetries in $D^0$ decays to $CP$ eigenstates such as $K_S{\pi }^0$ and others. Finally we demonstrate that with light KK masses, $\sim 3\mathrm{T}\mathrm{e}\mathrm{V}$, the above class of models with anarchic 5D Yukawas has a “$CP$ problem” since contributions to the neutron electric dipole moment are roughly 20 times larger than the current experimental bound. Using $\mathrm{A}\mathrm{d}\mathrm{S}/\mathrm{C}\mathrm{F}\mathrm{T}$ correspondence, these extra-dimensional models are dual to a purely 4D strongly coupled conformal Higgs sector thus enhancing their appeal.

In the context of the littlest Higgs (LH) model, we study single production of the new gauge bosons $B_H$, $Z_H$ and $W_H^{\pm }$ via $e^{-}\gamma$ collisions and discuss the possibility of detecting these new particles in the TeV energy $e^{+}{e}^{-}$ collider (LC). We find that these new particles can not be detected via the $e^{-}\nu \nu$ signal in all of the parameter space preferred by the electroweak precision data. However, the heavy gauge bosons $B_H$ and $Z_H$ may be observed via the decay channel $B_H(Z_H)\to l^{+}{l}^{-}$ in wide range of the parameter space.

The generalized dynamics describing the propagation of neutrinos in randomly fluctuating media is analyzed: It takes into account matter-induced, decoherence phenomena that go beyond the standard Mikheyev-Smirnov-Wolfenstein (MSW) effect. A widely adopted density fluctuation pattern is found to be physically untenable: A more general model needs to be instead considered, leading to flavor changing effective neutrino-matter interactions. They induce new, dissipative effects that modify the neutrino oscillation pattern in a way amenable to a direct experimental analysis.

To a first approximation, the quark mixing matrix has ${\theta }_{13}^q={\theta }_{23}^q=0$, whereas the lepton mixing matrix has ${\theta }_{23}^l=\pi /4$. We show how this structure may be understood if the family symmetry is $Q_8$, the quaternion group of eight elements. We find three viable scenarios for the Majorana neutrino mass matrix, each depending on four parameters and predicting a specific mass spectrum. The phenomenology of the two Higgs doublets which generate the Yukawa sector is analyzed and testable predictions are derived. We discuss also the closely related model based on $D_4$, the symmetry group of the square.

A spin $\frac{1}{2}$ particle propagating in a de Sitter background has a one parameter family of states which transform covariantly under the isometry group of the background. These states are the fermionic analogues of the $\alpha$-vacua for a scalar field. We shall show how using a point-source propagator for a fermion in an $\alpha$-state produces divergent perturbative corrections. These corrections cannot be used to cancel similar divergences arising from scalar fields in bosonic $\alpha$-vacua since they have an incompatible dependence on the external momenta. The theory can be regularized by modifying the propagator to include an antipodal source.

According to most inflationary models, fluctuations that are of cosmological size today started out much smaller than any plausible cutoff length such as the string or Planck lengths. It has been shown that this could open an experimental window for testing models of the short-scale structure of space-time. The observability of effects hinges crucially, however, on the initial conditions imposed on the new comoving modes which are continually being created at the cutoff length scale. Here, we address this question while modeling space-time as obeying the string and quantum gravity inspired minimum length uncertainty principle. We find that the usual strategy for determining the initial conditions faces an unexpected difficulty because it involves reformulating the action and discarding a boundary term: We find that actions that normally differ merely by a boundary term can differ significantly when the minimum length is introduced. This is possible because the introduction of a minimum length comes with an ordering ambiguity much like the ordering ambiguity that arises with the introduction of $\hslash$ in the process of quantization.

It is known that baryon-number inhomogeneities may arise as a consequence of electroweak baryogenesis. Their geometry, size, and amplitude depend on the parameters that characterize the baryogenesis mechanism, as well as on those that determine the phase transition dynamics. We investigate this parametric dependence. We show that in the case of the minimal supersymmetric standard model, the geometry of the inhomogeneities most probably consists of spherical regions of high density surrounded by low-density walls, in contrast to the case of the minimal standard model. In this supersymmetric extension, we find that density contrasts of up to a factor of 100 may arise. This amplitude increases for higher values of the latent heat or lower values of the bubble wall tension and can be significantly larger in different extensions of the standard model. Such inhomogeneities may thus affect the dynamics of the subsequent quark-hadron-phase transition.

We study the pentaquark $uudd\overline{s}$ with $J=3/2$ and $I=1$ (${\Theta }^{++}$) in the QCD sum rule approach. We derive the QCD sum rules for positive and negative parity states of the pentaquark. The QCD sum rule predicts that there exists ${\Theta }^{++}$ with negative parity and its mass is $1.5\sim 1.6$ GeV. The negative parity ${\Theta }^{++}$ can be extremely narrow, since it lies much below the $\Delta K$ threshold and the decay into $NK$ state is strongly suppressed due to the $D$-wave centrifugal barrier. Also, the possibility of the existence of the ${\Theta }^{++}$ with positive parity is not excluded. Although it nearly degenerates with the negative parity state, it may be broader than the negative parity state.

We analyze the fluctuations of the dressed sliver solution found in a previous paper, hep-th/0311198, in the operator formulation of Vacuum String Field Theory. We derive the tachyon wave function and then analyze the higher level fluctuations. We show that the dressing is responsible for implementing the transversality condition on the massless vector. In order to consistently deal with the singular $k=0$ mode we introduce a string midpoint regulator and we show that it is possible to accommodate all the open string states among the solutions to the linearized equations of motion. We finally show how the dressing can give rise to the correct ratio between the energy density of the dressed sliver and the brane tension computed via the three-tachyons-coupling.

We demonstrate the existence of gravitational critical phenomena in higher dimensional electrovac bubble spacetimes. To this end, we study linear fluctuations about families of static, homogeneous spherically symmetric bubble spacetimes in Kaluza-Klein theories coupled to a Maxwell field. We prove that these solutions are linearly unstable and posses a unique unstable mode. We further show that the associated growth rate depends only on the mass per unit length of the background solution. Additionally, by a double analytical continuation this mode can be seen to correspond to marginally stable stationary modes of perturbed black strings whose periods are integer multiples of the Gregory-Laflamme critical length. This allow us to rederive recent results about the behavior of the critical mass for large dimensions and to generalize them to charged black string cases.

In the context of the Penrose/Berenstein-Maldacena-Nastase (BMN) limit of the AdS/CFT correspondence, we consider four-impurity BMN operators in Yang-Mills theory and demonstrate explicitly their correspondence to four-oscillator states in string theory. Using the dilatation operator on the gauge-theory side of the correspondence, we calculate matrix elements between four-impurity states. Since conformal dimensions of gauge-theory operators correspond to light-cone energies of string states, these matrix elements may be compared with the string-theory light-cone Hamiltonian matrix elements calculated in the plane-wave background using the string field theory vertex. We find that the two calculations agree, extending the cases of two- and three-impurity operators considered in the literature using BMN gauge-theory quantum mechanics. The results are also in agreement with calculations in the literature based on perturbative gauge-theory methods.

Keeping Einstein's equations in second order form can be appealing for computational efficiency, because of the reduced number of variables and constraints. Stability issues emerge, however, which are not present in first order formulations. We show that a standard discretization of the second order “shifted” wave equation leads to an unstable semidiscrete scheme if the shift parameter is too large. This implies that discretizations obtained using integrators such as Runge-Kutta, Crank-Nicholson, and leapfrog are unstable for any fixed value of the Courant factor. We argue that this situation arises in numerical relativity, particularly in simulations of spacetimes containing black holes, and discuss several ways of circumventing this problem. We find that the first order reduction in time based on Arnowitt-Deser-Misner-type variables is very effective.

Recently a class of static spherical black hole solutions with scalar hair was found in four and five dimensional gauged supergravity with modified, but anti-de Sitter (AdS) invariant boundary conditions. These black holes are fully specified by a single conserved charge, namely, their mass, which acquires a contribution from the scalar field. Here we report on a more detailed study of some of the properties of these solutions. A thermodynamic analysis shows that in the canonical ensemble the standard Schwarzschild-AdS black hole is stable against decay into a hairy black hole. We also study the stability of the hairy black holes and find there always exists an unstable radial fluctuation, in both four and five dimensions. We argue, however, that Schwarzschild-AdS is probably not the end state of evolution under this instability.

We investigate the role of a suitable interaction between a matter fluid and a phantom field for the coincidence problem. There exists a stationary scaling solution which is a stable attractor at late times. Furthermore, the cosmic doomsday is avoided in one region of the parameter space.