We consider the Casimir effect of the electromagnetic field in a higher-dimensional spacetime of the form $M\times \mathcal{N}$, where $M$ is the four-dimensional Minkowski spacetime and $\mathcal{N}$ is an $n$-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in $M$ is large. It is found that if the separation between the plates is much smaller than the size of $\mathcal{N}$, the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the ($4+n$)-dimensional Minkowski spacetime. However, if the size of $\mathcal{N}$ is much smaller than the separation between the plates, the leading term of the Casimir force is $1+h/2$ times the Casimir force on a pair of large parallel plates in the four-dimensional Minkowski spacetime, where $h$ is the first Betti number of $\mathcal{N}$. In the limit the manifold $\mathcal{N}$ vanishes, one does not obtain the Casimir force in the four-dimensional Minkowski spacetime if $h$ is nonzero. Therefore the data obtained from Casimir experiments suggest that the first Betti number of the extra dimensions should be zero.

We calculate quarkonium binding energies using a realistic complex-valued potential for both an isotropic and anisotropic quark-gluon plasma. We determine the disassociation temperatures of the ground and first excited states considering both the real and imaginary parts of the binding energy. We show that the effect of momentum-space anisotropy is smaller on the imaginary part of the binding energy than on the real part of the binding energy. In the case that one assumes an isotropic plasma, we find disassociation temperatures for the $J/\psi$, ${\rm Y}$, and ${\chi }_b$ of $2.3T_c$, $2.9T_c$, and $1.8T_c$, respectively. We find that a finite oblate momentum-space anisotropy increases the disassociation temperature for all states considered and results in a splitting of the $p$-wave states associated with the ${\chi }_b$ first excited state of bottomonium.

We present a class of solutions of the $C{P}^N$ model in ($3+1$) dimensions. We suggest that they represent vortexlike configurations. We also discuss some of their properties. We show that some configurations of vortices have a divergent energy per unit length while for the others such an energy has a minimum for a very special orientation of vortices. We also discuss the Noether charge densities of these vortices.

We study a consistent infrared and ultraviolet regularization scheme for the cosmological perturbations. The infrared divergences are cured by assuming that the Universe undergoes a transition between a nonsingular preinflationary, radiation-dominated phase and a slow-roll inflationary evolution. The ultraviolet divergences are eliminated via adiabatic subtraction. A consistent regularization of the field fluctuations through this transition is obtained by performing a mode matching for both the gauge invariant Mukhanov variable and its adiabatic expansion. We show that these quantities do not generate ultraviolet divergences other than the standard ones, when evolving through the matching time. We also show how the DeWitt-Schwinger expansion, which can be used to construct the counter-terms regularizing the ultraviolet divergences, ceases to be valid well before horizon exit of the scales of interest. Thus, such counter-terms should not be used beyond the time of the horizon exit and it is unlikely that the observed power spectrum is modified by adiabatic subtraction, as claimed in some literature. On the contrary, the infrared regularization might have an impact on the observed spectrum, and we briefly discuss this possibility.

We study the $d=11$ gravity dual ${\mathrm{AdS}}_4\times N(1,1)$ of the $d=3$ $\mathcal{N}=3$ flavored Chern-Simons-matter theory. In the dual gravity side, we analyze the M5-brane filling ${\mathrm{AdS}}_3$ inside ${\mathrm{AdS}}_4$ and derive the quantized Hall conductivity of the dual gauge theory. In the gauge theory side, this M5-brane intersects the gauge theory at the codimension-one defect.

We study a modified version of the Ginzburg-Landau model suggested by Ward and show that Hopfions exist in it as stable static solutions, for values of the Hopf invariant up to at least 7. We also find that their properties closely follow those of their counterparts in the Faddeev-Skyrme model. Finally, we lend support to Babaev’s conjecture that longer core lengths yield more stable solitons and propose a possible mechanism for constructing Hopfions in pure Ginzburg-Landau model.

The optimal reconstruction of cosmic metric perturbations and other signals requires knowledge of their power spectra and other parameters. If these are not known a priori, they have to be measured simultaneously from the same data used for the signal reconstruction. We formulate the general problem of signal inference in the presence of unknown parameters within the framework of information field theory. To solve this, we develop a generic parameter-uncertainty renormalized estimation (PURE) technique. As a concrete application, we address the problem of reconstructing Gaussian signals with unknown power-spectrum with five different approaches: (i) separate maximum-a-posteriori power-spectrum measurement and subsequent reconstruction, (ii) maximum-a-posteriori reconstruction with marginalized power-spectrum, (iii) maximizing the joint posterior of signal and spectrum, (iv) guessing the spectrum from the variance in the Wiener-filter map, and (v) renormalization flow analysis of the field-theoretical problem providing the PURE filter. In all cases, the reconstruction can be described or approximated as Wiener-filter operations with assumed signal spectra derived from the data according to the same recipe, but with differing coefficients. All of these filters, except the renormalized one, exhibit a perception threshold in case of a Jeffreys prior for the unknown spectrum. Data modes with variance below this threshold do not affect the signal reconstruction at all. Filter (iv) seems to be similar to the so-called Karhune-Loève and Feldman-Kaiser-Peacock estimators for galaxy power spectra used in cosmology, which therefore should also exhibit a marginal perception threshold if correctly implemented. We present statistical performance tests and show that the PURE filter is superior to the others, especially if the post-Wiener-filter corrections are included or in case an additional scale-independent spectral smoothness prior can be adopted.

We calculate the one-loop graviton vacuum polarization induced by a massless, nonminimally coupled scalar field on Minkowski background. We make use of the Schwinger-Keldysh formalism, which allows us to study time dependent phenomena. As an application we compute the leading quantum correction to the Newtonian potential of a point particle. The novel aspect of the calculation is the use of the Schwinger-Keldysh formalism, within which we calculate the time transients induced by switching on the graviton-scalar coupling.

The physical modes of a recently proposed $D$-dimensional “critical gravity”, linearized about its anti-de Sitter vacuum, are investigated. All “log mode” solutions, which we categorize as “spin-2” or “Proca”, arise as limits of the massive spin-2 modes of the noncritical theory. The linearized Einstein tensor of a spin-2 log mode is itself a ‘nongauge’ solution of the linearized Einstein equations whereas the linearized Einstein tensor of a Proca mode takes the form of a linearized general coordinate transformation. Our results suggest the existence of a holographically dual logarithmic conformal field theory.

We analyze the gravitational perturbations induced by particles falling into a three dimensional, asymptotically AdS black hole geometry. More specifically, we solve the linearized perturbation equations obtained from the geodesic motion of a ringlike distribution of test particles in the BTZ background. This setup ensures that the $U(1)$ symmetry of the background is preserved. The nonasymptotic flatness of the background raises difficulties in attributing the significance of energy and angular momentum to the conserved quantities of the test particles. This issue is well known but, to the best of our knowledge, has never been addressed in the literature. We confirm that the naive expressions for energy and angular momentum are the correct definitions. Finally, we put an asymptotically AdS version of the weak cosmic censorship to a test: by attempting to overspin the BTZ black hole with test particles it is found that the black hole cannot be spun-up past its extremal limit.

We study the Hamiltonian formulation of $f(R)$ theories of gravity both in metric and in Palatini formalism using their classical equivalence with Brans-Dicke theories with a nontrivial potential. The Palatini case, which corresponds to the $\omega =-3/2$ Brans-Dicke theory, requires special attention because of new constraints associated with the scalar field, which is nondynamical. We derive, compare, and discuss the constraints and evolution equations for the $\omega =-3/2$ and $\omega \ne -3/2$ cases. Based on the properties of the constraint and evolution equations, we find that, contrary to certain claims in the literature, the Cauchy problem for the $\omega =-3/2$ case is well formulated and there is no reason to believe that it is not well posed in general.

We study linear metric perturbations around a spherically symmetric static spacetime for general $f(R,\mathcal{G})$ theories, where $R$ is the Ricci scalar and $\mathcal{G}$ is the Gauss-Bonnet term. We find that, unless the determinant of the Hessian of $f(R,\mathcal{G})$ is zero, even-type perturbations have a ghost for any multipole mode. In order for these theories to be plausible alternatives to general relativity, the theory should satisfy the condition that the ghost is massive enough to effectively decouple from the other fields. We study the requirement on the form of $f(R,\mathcal{G})$ which satisfies this condition. We also classify the number of propagating modes both for the odd-type and the even-type perturbations and derive the propagation speeds for each mode.

Building initial conditions for generic binary black-hole evolutions which are not affected by initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure which consists of evolving the binary black hole for a couple of orbits, estimating the resulting eccentricity, and then restarting the simulation with corrected initial conditions. The presence of spins can complicate this procedure. As predicted by post-Newtonian theory, spin-spin interactions and precession prevent the binary from moving along an adiabatic sequence of spherical orbits, inducing oscillations in the radial separation and in the orbital frequency. For single-spin binary black holes these oscillations are a direct consequence of monopole-quadrupole interactions. However, spin-induced oscillations occur at approximately twice the orbital frequency, and therefore can be distinguished and disentangled from the initial spurious eccentricity which occurs at approximately the orbital frequency. Taking this into account, we develop a new eccentricity-removal procedure based on the derivative of the orbital frequency and find that it is rather successful in reducing the eccentricity measured in the orbital frequency to values less than ${10}^{-4}$ when moderate spins are present. We test this new procedure using numerical-relativity simulations of binary black holes with mass ratios 1.5 and 3, spin magnitude 0.5, and various spin orientations. The numerical simulations exhibit spin-induced oscillations in the dynamics at approximately twice the orbital frequency. Oscillations of similar frequency are also visible in the gravitational-wave phase and frequency of the dominant $l=2$, $m=2$ mode.

The aim of this paper is to explore $D$-dimensional theories of pure gravity whose space of solutions contains a certain class of anti-de Sitter waves including, in particular, Schrödinger invariant spacetimes. This leads to consider higher-order theories, and the natural case to start with is to analyze generic square-curvature corrections to the Einstein-Hilbert action. In this case, the Schrödinger invariant sector in the space of solutions arises for a special relation between the coupling constants appearing in the action. On the other hand, besides the Schrödinger invariant configurations, logarithmic branches similar to those of the so-called log-gravity are also shown to emerge for another special choice of the coupling constants. Interestingly enough, these log solutions can be interpreted as the superposition of the massless mode of general relativity and two scalar modes that saturate the Breitenlohner-Freedman (BF) bound of the AdS space on which they propagate. These solutions are higher-dimensional analogues of those appearing in three-dimensional massive gravities with relaxed ${\mathrm{AdS}}_3$ asymptotic, which are candidates to be gravity duals for logarithmic conformal field theories (CFTs). Other sectors of the space of solutions of higher-curvature theories correspond to oscillatory configurations, which happen to be below the BF bound. Also, there is a fully degenerated sector, for which any wave profile is admitted. We comment on the relation between this degeneracy and the nonrenormalizability of the dynamical exponent of the Schrödinger spaces. Our analysis also includes more general gravitational actions with nonpolynomial corrections consisting of arbitrary functions of the square-curvature invariants. By establishing a correspondence with the quadratic gravity model, the same sectors of solutions are shown to exist for this more general family of theories. We finally consider the parity-violating Chern-Simons modified gravity in four dimensions, for which we derive both the Schrödinger invariant as well as the logarithmic sectors.

If the dark matter of our Galaxy is composed of nuggets of quarks or antiquarks in a color superconducting phase there will be a small but nonzero flux of these objects through the Earth’s atmosphere. A nugget of quark matter will deposit only a small fraction of its kinetic energy in the atmosphere and is likely to be undetectable. If however the impacting object is composed of antiquarks, the energy deposited can be quite large. In this case nuclear annihilations within the nugget will trigger an extensive air shower the particle content of which is similar to that produced by an ultrahigh energy cosmic ray. This paper gives a qualitative description of the basic properties of such a shower. Several distinctions from an air shower initiated by a single ultrahigh energy nucleus will be described, allowing these events to be distinguished from the cosmic ray background. The subtlety of these features may mean that some fraction of the high energy cosmic ray spectrum may in fact be due to this type of dark matter interaction. The estimated flux of dark matter nuggets and the energy deposited in the atmosphere are such that the Pierre Auger Observatory may prove an ideal facility to place constraints on the flux of heavy quark matter objects. This paper attempts to highlight the best techniques to search for a quark matter signature through an extensive air shower signal.

We explore the possibility that a new interaction between muons and protons is responsible for the discrepancy between the CODATA value of the proton-radius and the value deduced from the measurement of the Lamb shift in muonic hydrogen. We show that a new force carrier with roughly MeV-mass can account for the observed energy-shift as well as the discrepancy in the muon anomalous magnetic moment. However, measurements in other systems constrain the couplings to electrons and neutrons to be suppressed relative to the couplings to muons and protons, which seems challenging from a theoretical point of view. One can nevertheless make predictions for energy shifts in muonic deuterium, muonic helium, and true muonium under the assumption that the new particle couples dominantly to muons and protons.

We propose a warm inflationary model in the context of relativistic D-brane inflation in a warped throat, which has Dirac-Born-Infeld (DBI) kinetic term and is coupled to radiation through a dissipation term. The perturbation freezes at the sound horizon and the power spectrum is determined by a combination of the dissipative parameter and the sound speed parameter. The thermal dissipation ameliorates the eta problem and softens theoretical constraints from the extra-dimensional volume and from observational bounds on the tensor-to-scalar ratio. The warm DBI model can lead to appreciable non-Gaussianity of the equilateral type. As a phenomenological model, ignoring compactification constraints, we show that large-field warm inflation models do not necessarily yield a large tensor-to-scalar ratio.

The appearance of spin-1 resonances associated with the electroweak symmetry breaking sector is expected in many extensions of the standard model. We analyze the CERN Large Hadron Collider potential to probe the spin of possible new charged and neutral vector resonances through the purely leptonic processes $pp\to Z^{\prime }\to {\ell }^{+}{\ell }^{\prime -}{\cancel{E}}_T$, and $pp\to W^{\prime }\to {\ell }^{\prime \pm }{\ell }^{+}{\ell }^{-}{\cancel{E}}_T$, with $\ell$, ${\ell }^{\prime }=e$ or $\mu$. We perform a model-independent analysis and demonstrate that the spin of the new states can be determined with 99% C.L. in a large fraction of the parameter space where these resonances can be observed with $100{\mathrm{fb}}^{-1}$. We show that the best sensitivity to the spin is obtained by directly studying correlations between the final state leptons, without the need of reconstructing the events in their center-of-mass frames.

We propose a new way to determine the squark mass based on the shape of dijet invariant mass distribution of supersymmetry dijet events at the Large Hadron Collider. Our algorithm, which is based on event kinematics, requires that the branching ratio $B(\tilde{q}\to q{\tilde{Z}}_1)$ is substantial for at least some types of squarks, and that $m_{{\tilde{Z}}_1}^2/m_{\tilde{q}}^2\ll 1$. We select dijet events with no isolated leptons, and impose cuts on the total jet transverse energy, $E_T^{\mathrm{tot}}=E_T(j_1)+E_T(j_2)$, on $\alpha =E_T(j_2)/m_{jj}$, and on the azimuthal angle between the two jets to reduce standard model backgrounds. The shape of the resulting dijet mass distribution depends sensitively on the squark mass, especially if the integrated luminosity is sufficient to allow a hard enough cut on $E_T^{\mathrm{tot}}$ and yet leave a large enough signal to obtain the $m_{jj}$ distribution. We simulate the signal and standard model backgrounds for $100{\mathrm{fb}}^{-1}$ integrated luminosity at 14 TeV requiring $E_T^{\mathrm{tot}}>700\mathrm{GeV}$. We show that it should be possible to extract $m_{\tilde{q}}$ to within about 3% at 95% confidence level—similar to the precision obtained using $m_{T2}$—from the dijet mass distribution if $m_{\tilde{q}}\sim 650\mathrm{GeV}$, or to within $\sim 5\%$ if $m_{\tilde{q}}\sim 1\mathrm{TeV}$.

We study $CP$ violation in the two-body decay of a scalar tau into a neutralino and a tau, which should be probed at the LHC and ILC. From the normal tau polarization, a $CP$ asymmetry is defined which is sensitive to the $CP$ phases of the trilinear scalar coupling parameter $A_{\tau }$, the gaugino mass parameter $M_1$, and the Higgsino mass parameter $\mu$, in the stau-neutralino sector of the minimal supersymmetric standard model. Asymmetries of more than 70% are obtained in scenarios with strong stau mixing. As a result, detectable $CP$ asymmetries in stau decays at the LHC are found, motivating further detailed experimental studies for probing the supersymmetry $CP$ phases.