In $\mathcal{N}=4$ super-Yang-Mills theory at large $N$, large $\lambda$, and finite temperature, the value of the Wilson-Maldacena loop wrapping the Euclidean time circle (the Polyakov-Maldacena loop, or PML) is computed by the area of a certain minimal surface in the dual supergravity background. This prescription can be used to calculate the free energy as a function of the PML (averaged over the spatial coordinates), by introducing into the bulk action a Lagrange multiplier term that fixes the (average) area of the appropriate minimal surface. This term, which can also be viewed as a chemical potential for the PML, contributes to the bulk stress tensor like a string stretching from the horizon to the boundary (smeared over the angular directions). We find the corresponding “hedgehog” black hole solutions numerically, within an $SO(6)$-preserving ansatz, and derive part of the free energy diagram for the PML. As a warm-up problem, we also find exact solutions for hedgehog black holes in pure gravity, and derive the free energy and phase diagrams for that system.

This article examines how a breakdown of a locally Lorentz-invariant, pointlike description of nature at tiny space-time intervals would translate into a distinctive set of signals in the primordial power spectrum generated by inflation. We examine the leading irrelevant operators that are consistent with the spatial translations and rotations of a preferred, isotropically expanding, background. A few of the resulting corrections to the primordial power spectrum do not have the usual oscillatory factor, which is sometimes taken to be characteristic of a “trans-Planckian” signal. Perhaps more interestingly, one of these leading irrelevant operators exactly reproduces a correction to the power spectrum that occurs in effective descriptions of the state of the field responsible for inflation.

The purpose of this work is twofold. Working in the framework of $(1+1)D$ Lorentz violating field theories, we will investigate first the general claim that fermionic interactions may be equivalent to a deformation of the canonical structure of the theory. Second, the deformed theory will be studied using duality reasoning to address the behavior of the infrared and ultraviolet regimes.

This paper is an investigation of the stability of some ideal stars. It is intended as a study in general relativity, with emphasis on the coupling to matter, aimed at a better understanding of strong gravitational fields and “black holes.” This contrasts with the usual attitude in astrophysics, where Einstein’s equations are invoked as a refinement of classical thermodynamics and Newtonian gravity. Our work is based on action principles for systems of metric and matter fields, well-defined relativistic field models that we hope may represent plausible types of matter. The thermodynamic content must be extracted from the theory itself. When the flow of matter is irrotational, and described by a scalar density, we are led to differential equations that differ little from those of Tolman, but they admit a conserved current, and stronger boundary conditions that affect the matching of the interior solution to an external metric and imply a relation of mass and radius. We propose a complete revision of the treatment of boundary conditions. An ideal star in our terminology has spherical symmetry and an isentropic equation of state, $p=a{\rho }^{\gamma }$, $a$ and $\gamma$ piecewise constant. In our first work it was assumed that the density vanished beyond a finite distance from the origin and that the metric is to be matched at the boundary to an exterior Schwartzchild metric. But it is difficult to decide what the boundary conditions should be and we are consequently skeptical of the concept of a fixed boundary. We investigate the double polytrope, characterized by a polytropic index $n\le 3$, in the bulk of the star and a value larger than five in an outer atmosphere that extends to infinity. It has no fixed boundary but a region of critical density where the polytropic index changes from a value that is appropriate for the bulk of the star to a value that provides a crude model for the atmosphere. The boundary conditions are now natural and unambiguous. The existence of a relation between mass and radius is confirmed, as well as an upper limit on the mass. The principal conclusion is that all the static configurations are stable. There is a solution that fits the Sun. The masses of white dwarfs respect the Chandrasekhar limit. The application to neutron stars has surprising aspects.

In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962), p. 227; arXiv:gr-qc/0405109]. The implementation is made with the aid of a symmetric stress-energy tensor and not a 4-dimensional covariant action functional. The formalism is valid to terms linear in the single spin variables and up to and including the next-to-leading order approximation in the gravitational spin-interaction part. The field-source terms for the spinning particles occurring in the Hamiltonian are obtained from their expressions in Minkowski space with canonical variables through 3-dimensional covariant generalizations as well as from a suitable shift of projections of the curved spacetime stress-energy tensor originally given within covariant spin supplementary conditions. The applied coordinate conditions are the generalized isotropic ones introduced by Arnowitt, Deser, and Misner. As applications, the Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling, recently obtained by Damour, Jaranowski, and Schäfer [Phys. Rev. D 77, 064032 (2008)], is rederived and the derivation of the next-to-leading order gravitational spin(1)-spin(2) Hamiltonian, shown for the first time in [J. Steinhoff, S. Hergt, and G. Schäfer, Phys. Rev. D 77, 081501(R) (2008)], is presented.

We construct an equation of state including the hadron-quark phase transition. The mixed phase is obtained by the Gibbs conditions for finite temperature. We adopt the equation of state based on the relativistic mean field theory for the hadronic phase, taking into account pions. As for the quark phase, the MIT bag model of the deconfined 3-flavor strange quark matter is used. As a result, our equation of state is thermodynamically stable and qualitatively exhibits the desired properties of hadron-quark mixed matter, such as the temperature dependence of the transition density. The pions raise the transition density because they make the equation of state softer. Using the equation of state constructed here, we study its astrophysical implications. The maximum mass of compact stars is investigated, and our equation of state is consistent with recent observations. We also compute the collapse of a massive star with 100 solar masses ($M_{\odot }$) using our equation of state and find that the interval time from the bounce to the black hole formation becomes shorter for the model with pions and quarks. The pions and quarks affect the total energy of the emitted neutrinos because the duration time of the neutrino emission becomes shorter. The neutrino luminosity rises under the effect of pions since the density of the proto-neutron star becomes high.

The decay of the standard model Higgs boson into a single photon and a vector unparticle through a one-loop process is studied. For an intermediate-mass Higgs boson, this single photon plus unparticle mode can have a branching ratio comparable with the two-photon discovery mode. The emitted photon has a continuous energy spectrum encoding the nature of the recoil unparticle. It can be measured in precision studies of the Higgs boson after its discovery.

The recently discovered $X(3872)$ has many possible interpretations. We study the production of $X(3872)$ with PANDA at GSI for the antiproton-proton collision with two possible interpretations of $X(3872)$. One is as a loosely bound molecule of $D$ mesons, while another is a $2P$ charmonium state ${\chi }_{\mathrm{c}1(2P)}$. Using effective couplings we are able to give numerical predictions for the production near the threshold and the production associated with ${\pi }^0$. We also study the possible background near the threshold production for $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$. With the designed luminosity $1.5{\mathrm{fb}}^{-1}$ per year of PANDA we find that the event number of $p\overline{p}\to J/\psi {\pi }^{+}{\pi }^{-}$ near the threshold is at the order of ${10}^6–{10}^8$. Our study shows that two interpretations are distinguishable from the line shape of the production.

A nonperturbative renormalization group approach is used to calculate scaling functions for an $O(4)$ model in $d=3$ dimensions in the presence of an external symmetry-breaking field. These scaling functions are important for the analysis of critical behavior in the $O(4)$ universality class. For example, the finite-temperature phase transition in QCD with two flavors is expected to fall into this class. Critical exponents are calculated in local-potential approximation. Parametrizations of the scaling functions for the order parameter and for the longitudinal susceptibility are given. Relations from universal scaling arguments between these scaling functions are investigated and confirmed. The expected asymptotic behavior of the scaling functions predicted by Griffiths is observed. Corrections to the scaling behavior at large values of the external field are studied qualitatively. These scaling corrections can become large, which might have implications for the scaling analysis of lattice QCD results.

Mixed action lattice calculations allow for an additive lattice-spacing-dependent mass renormalization of mesons composed of one sea and one valence quark, regardless of the type of fermion discretization methods used in the valence and sea sectors. The value of the mass renormalization depends upon the lattice actions used. This mixed meson mass shift is an important lattice artifact to determine for mixed action calculations; because it modifies the pion mass, it plays a central role in the low-energy dynamics of all hadronic correlation functions. We determine the leading order, $\mathcal{O}(a^2)$, and next-to-leading order, $\mathcal{O}(a^2{m}_{\pi }^2)$, additive mass shift of valence-sea mesons for a mixed lattice action with domain-wall valence fermions and rooted staggered sea fermions, relevant to the majority of current large scale mixed action lattice efforts. We find that, on the asqtad-improved coarse MILC lattices, this additive mass shift is well parametrized in lattice units by $\Delta (am{)}^2=0.034(2)-0.06(2)(a{m}_{\pi }{)}^2$, which in physical units, using $a=0.125\mathrm{fm}$, corresponds to $\Delta (m{)}^2=(291\pm 8\mathrm{MeV}{)}^2-0.06(2)m_{\pi }^2$. In terms of the mixed action effective field theory parameters, the corresponding mass shift is given by $a^2{\Delta }_{\mathrm{Mix}}=(316\pm 4\mathrm{MeV}{)}^2$ at leading order plus next-to-leading order corrections including the necessary chiral logarithms for this mixed action calculation, determined in this work. Within the precision of our calculation, one cannot distinguish between the full next-to-leading order effective field theory analysis of this additive mixed meson mass shift and the parametrization given above.

We calculate the next-to-next-to-leading order $\mathcal{O}({\alpha }_s^4)$ one-loop squared corrections to the production of heavy quark pairs in quark-antiquark annihilations. These are part of the next-to-next-to-leading order $\mathcal{O}({\alpha }_s^4)$ radiative QCD corrections to this process. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in the dimensional regularization scheme. We have found very intriguing factorization properties for the finite part of the amplitudes.

Parametrization of the quark and lepton mixing matrices is the first attempt to understand the mixing of fermions. In this work, we parametrize the quark and lepton mixing matrices with the help of quark-lepton complementarity in a tribimaximal pattern of the lepton mixing matrix. In this way, we combine the parametrization of the two matrices. We apply this new parametrization to several physical quantities, and show its simplicity in the expression of, e.g., the Jarlskog parameter of $CP$ violation.

We present the first measurement of two-particle momentum correlations in jets produced in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. Results are obtained for charged particles within a restricted cone with an opening angle of 0.5 radians around the jet axis and for events with dijet masses between 66 and $563\mathrm{GeV}/c^2$. A comparison of the experimental data to theoretical predictions obtained for partons within the framework of resummed perturbative QCD in the next-to-leading log approximation shows that the parton momentum correlations survive the hadronization stage of jet fragmentation, giving further support to the hypothesis of local parton-hadron duality. The extracted value of the next-to-leading-log-approximation parton shower cutoff scale $Q_{\mathrm{eff}}$ set equal to ${\Lambda }_{\mathrm{QCD}}$ is found to be $({1.4}_{-0.7}^{+0.9})\times 100\mathrm{MeV}$.

Several cosmological models have been proposed in order to explain the current acceleration of the Universe. Recently, the normal branch of the DGP (after Dvali, Gabadadze, and Porrati) brane model with a generalized Chaplygin gas was studied as a model which can cross the phantom divide line avoiding the future singularity. In the present work, we wish to address the question of whether or not the aforementioned model has a better fit to supernovae data compared to cold dark matter with a cosmological constant, the (generalized) Chaplygin gas, and the DGP model with the self-accelerating branch without extra fluid for dark energy. We have found that the Chaplygin-DGP model has the worst fit, while the two-fluid model with Chaplygin gas and dust (baryons) has the best fit among the theoretical cosmological models considered here.

The Euclidean path integral quite often involves an action that is not completely real, i.e. a complex action. This occurs when the Minkowski action contains $t$-odd $CP$-violating terms. This usually consists of topological terms, such as the Chern-Simons term in odd dimensions, the Wess-Zumino term, the $\theta$ term or Chern character in 4-dimensional gauge theories, or other topological densities. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. It also occurs when the action contains fermions, the fermion path integral being in general a sum over positive and negative real numbers. Negative numbers correspond to the exponential of $i\pi$ and hence indicate the presence of an imaginary term in the action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, this procedure is not followed. Rather, only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory, a procedure that can lead to incorrect results. In this article we present a simple example to illustrate this point. The example consists of $N$ scalar fields in $0+1$ dimensions interacting with a $U(1)$ gauge field in the presence of a Chern-Simons term. In this example the path integral can be done exactly, the procedure of deformation of the contour of path integration can be done explicitly and the standard method of only taking into account the real part of the action can be followed. We show that the standard method does not give a correct perturbative expansion. The implications of our work include perturbation theory in the standard model which is $CP$-violating, but also for calculations in the presence of topological terms which have given rise to radical changes in the spectrum of the theory.

A new time-dependent, scale-independent parameter, $\varpi$, is employed in a phenomenological model of the deviation from general relativity in which the Newtonian and longitudinal gravitational potentials slip apart on cosmological scales as dark energy, assumed to be arising from a new theory of gravitation, appears to dominate the Universe. A comparison is presented between $\varpi$ and other parametrized post-Friedmannian models in the literature. The effect of $\varpi$ on the cosmic microwave background anisotropy spectrum, the growth of large-scale structure, the galaxy weak-lensing correlation function, and cross correlations of cosmic microwave background anisotropy with galaxy clustering are illustrated. Cosmological models with conventional maximum likelihood parameters are shown to find agreement with a narrow range of gravitational slip.

Understanding the dynamics around rotating black holes is imperative to the success of future gravitational wave observatories. Although integrable in principle, test-particle orbits in the Kerr spacetime can also be elaborate, and while they have been studied extensively, classifying their general properties has been a challenge. This is the first in a series of papers that adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We define a taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strong-field regime. Instead, eccentric orbits trace out precessions of multileaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some point in the strong-field regime past which zoom-whirl behavior becomes unavoidable. Finally, we sketch the potential application of the taxonomy to problems of astrophysical interest, in particular its utility for computationally intensive gravitational wave calculations.

We study the energy losses of the tau lepton in matter through electromagnetic processes at ultrahigh energy. We use both a stochastic and a continuous framework to treat these interactions and compare the flux of tau leptons propagated after some amount of matter. We discuss the accuracy of the approximation of continuous energy losses by studying the propagation in standard rock of taus with both monoenergetic and power-law injection spectra. Despite fluctuations introduced by the stochastic nature of the radiative processes, we show that the continuous approximation leads to the same results for power-law injection spectra.

It was recently found that the decay of the inflaton and the supersymmetry breaking field produces many gravitinos in the gravity mediation scenario. These discoveries showed that many inflation models such as chaotic, (smooth) hybrid, topological, and new inflation models are disfavored. Under these circumstances we search for a successful inflation model and find that the inverted hybrid inflation models can solve the gravitino overproduction problem by their distinctive shape of the potential. Furthermore, we show that this inflation model simultaneously can explain the observed baryon asymmetry through the nonthermal leptogenesis and is consistent with the WMAP results, that is, $n_s={0.951}_{-0.019}^{+0.015}$ and the negligible tensor to scalar ratio.

As it is well known, top quark decays are of particular interest as a means to test the standard model (SM) predictions, these include the dominant ($t\to b+W$), the Cabibbo-Kobayashi-Maskawa (CKM)-suppressed process $t\to cWW$, and the rare decays ($t\to cV$, $cVV$, $c{\varphi }^0$, $bWZ$). As all of them are highly suppressed, they become an excellent window to probe the predictions of theories beyond the SM. In this paper, we evaluate the corrections from new physics to the CKM-suppressed SM top quark decay $t\to q+W(q=d,s)$, both within an effective model with right-handed currents and for the minimal SUSY extension of the SM. We also discuss the perspectives to probe those predictions at the International Linear Collider.