We propose a generalized Skyrme-Faddeev type theory with an additional scalar field. In a special case of model parameters, one has a theory which admits exact knot solutions given by a class of exact toroidal solitons from the Aratyn-Ferreira-Zimerman (AFZ) integrable $C{P}^1$ model. In a general case, the theory admits an exact knot solution for a unit Hopf charge. For higher Hopf charges, we perform numeric analysis of the solutions and obtain estimates for the knot energies using an energy minimization procedure based on ansatz with AFZ field configurations and with rational functions. We show that AFZ configurations provide better approximate solutions. The corresponding knot energies are in good agreement with a standard law for the low energy bound, $E_H\simeq Q_H^{3/4}$.

It is shown that the Pais-Uhlenbeck oscillator with damping, considered by Nesterenko, is a special case of a more general oscillator that has not only a first order, but also a third order friction term. If the corresponding damping constants, $\alpha$ and $\beta$, are both positive and below certain critical values, then the system is stable. In particular, if $\alpha =-\beta$, then we have the unstable Nesterenko’s oscillator.

We study the topological Casimir effect, in which extra vacuum energy emerges as a result of the topological features of the theory, rather than due to the conventional fluctuations of the physical propagating degrees of freedom. We compute the corresponding topological term in quantum Maxwell theory defined on a compact manifold. Numerically, the topological effect is much smaller than the conventional Casimir effect. However, we argue that the topological Casimir effect is highly sensitive to an external magnetic field, which may help to discriminate it from the conventional Casimir effect. It is quite amazing that the external magnetic field plays the role of the $\theta$ state, similar to a $\theta$ vacuum in QCD, or $\theta =\pi$ in topological insulators.

The theory of string-like continuous curves and discrete chains have numerous important physical applications. Here we develop a general geometrical approach, to systematically derive Hamiltonian energy functions for these objects. In the case of continuous curves, we demand that the energy function must be invariant under local frame rotations, and it should also transform covariantly under reparametrizations of the curve. This leads us to consider energy functions that are constructed from the conserved quantities in the hierarchy of the integrable nonlinear Schrödinger equation. We point out the existence of a Weyl transformation that we utilize to introduce a dual hierarchy to the standard nonlinear Schrödinger equation hierarchy. We propose that the dual hierarchy is also integrable, and we confirm this to the first nontrivial order. In the discrete case the requirement of reparametrization invariance is void. But the demand of invariance under local frame rotations prevails, and we utilize it to introduce a discrete variant of the Zakharov-Shabat recursion relation. We use this relation to derive frame-independent quantities that we propose are the essentially unique and as such natural candidates for constructing energy functions for piecewise linear polygonal chains. We also investigate the discrete version of the Weyl duality transformation. We confirm that in the continuum limit the discrete energy functions go over to their continuum counterparts, including the perfect derivative contributions.

We consider the thermodynamics of rotating and charged asymptotically de Sitter (dS) black holes. Using Hamiltonian perturbation-theory techniques, we derive three different first-law relations including variations in the cosmological constant, and associated Smarr formulas that are satisfied by such spacetimes. Each first law introduces a different thermodynamic volume conjugate to the cosmological constant. We examine the relation between these thermodynamic volumes and associated geometric volumes in a number of examples, including Kerr-dS black holes in all dimensions and Kerr-Newman-dS black holes in $D=4$. We also show that the Chong-Cvetic-Lu-Pope solution of $D=5$ minimal supergravity—analytically continued to positive cosmological constant—describes black hole solutions of the Einstein-Chern-Simons theory and include such charged asymptotically de Sitter black holes in our analysis. In all these examples we find that the particular thermodynamic volume associated with the region between the black hole and cosmological horizons is equal to the naive geometric volume. Isoperimetric inequalities, which hold in the examples considered, are formulated for the different thermodynamic volumes and conjectured to remain valid for all asymptotically de Sitter black holes. In particular, in all examples considered, we find that for a fixed volume of the observable universe, the entropy is increased by adding black holes. We conjecture that this is true in general.

We study primordial gravitational waves in the Horava-Lifshitz theory of quantum gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear in order for the theory to be power-counting renormalizable and ultraviolet complete. Because of both parity violation and the nonadiabatic evolution of the modes due to a modified dispersion relationship, a large polarization of primordial gravitational waves becomes possible, and it could be well within the range of detection of the BB, TB and EB power spectra of the forthcoming cosmic microwave background observation, where T, E, and B stand, respectively, the different components of the polarization of the cosmic microwave background radiation.

We present the first constraints on the full parameter space of the Galileon modified gravity model, considering both the cosmological parameters and the coefficients which specify the additional terms in the Lagrangian due to the Galileon field, which we call the Galileon parameters. We use the latest cosmic microwave background measurements, along with distance measurements from supernovae and baryonic acoustic oscillations, performing a Monte Carlo Markov Chain exploration of the nine-dimensional parameter space. The integrated Sachs-Wolfe signal can be very different in Galileon models compared to standard gravity, making it essential to use the full cosmic microwave background data rather than the cosmic microwave background distance priors. We demonstrate that meaningful constraints are only possible in the Galileon parameter space after taking advantage of a scaling degeneracy. We find that the Galileon model can fit the Wilkinson microwave anisotropy probe 9-year results better than the standard $\Lambda$-cold dark matter model, but gives a slightly worse fit overall once lower redshift distance measurements are included. The best-fitting cosmological parameters (e.g., matter density, scalar spectral index, fluctuation amplitude) can differ by more than $2\sigma$ in the Galileon model compared with $\Lambda \mathrm{CDM}$. We highlight other potential constraints of the Galileon model using galaxy clustering and weak lensing measurements.

The nongauge vector field with as simple a Lagrangian as possible turned out to be an adequate tool for the macroscopic description of the main properties of dark matter. The dependence of the velocity of a star on the radius of the orbit $V(r)$—galaxy rotation curve—is derived analytically from the first principles completely within Einstein’s general relativity. Milgrom’s empirical modification of Newtonian dynamics in the nonrelativistic limit gets justified and specified in detail. In particular, the transition to a plateau is accompanied by damping oscillations. In the scale of a galaxy, and in the scale of the whole universe, the dark matter is described by a vector field with the same energy-momentum tensor. It is the evidence of the common physical nature. Now, when we have the general expression for the energy-momentum tensor of dark matter, it is possible to analyze its influence on the structure and evolution of superheavy stars and black holes.

An analysis of the Fermi gamma-ray space telescope data has recently revealed a resolved gamma-ray feature close to the galactic center which is consistent with monochromatic photons at an energy of about 130 GeV. If interpreted in terms of dark matter (DM) annihilating into $\gamma \gamma$ ($\gamma Z$, $\gamma h$), this would correspond to a DM particle mass of roughly 130 GeV (145 GeV, 155 GeV). The rate for these loop-suppressed processes, however, is larger than typically expected for thermally produced DM. Correspondingly, one would generically expect even larger tree-level production rates of standard model fermions or gauge bosons. Here, we quantify this expectation in a rather model-independent way by relating the tree level and loop amplitudes with the help of the optical theorem. As an application, we consider bounds from continuum gamma rays, radio, and antiproton data on the tree-level amplitudes and translate them into constraints on the loop amplitudes. We find that, independently of the DM production mechanism, any DM model aiming at explaining the line signal in terms of charged standard model particles running in the loop is in rather strong tension with at least one of these constraints, with the exception of loops dominated by top quarks. We stress that attempts to explain the 130 GeV feature with internal bremsstrahlung do not suffer from such difficulties.

The high positron production rate required to explain the flux of 511 keV gamma rays from the Galactic center has inspired many models in which dark matter creates positrons. These models include the annihilation of light dark matter and the scattering of dark matter with excited states (exciting dark matter). We show that existing cosmic microwave background data robustly constrain such models when the annihilation or scattering cross section is not velocity suppressed depending on the model of the Galactic dark matter halo. Upcoming data from the Planck mission can exclude the fiducial Via Lactea II halo model, which also provides a good fit to the 511 keV morphology. We additionally find combined constraints on exciting dark matter scattering and annihilation, and update constraints on the lifetimes of dark matter excited states. Finally, we apply constraints to models of dark matter decay in which produced positrons fall into the Galactic center and produce the 511 keV signal on their annihilation, demonstrating that most of the parameter space of interest is ruled out.

We have performed an in-depth concept study of a gravitational wave data analysis method which targets repeated long quasimonochromatic transients (triggers) from cosmic sources. The algorithm concept can be applied to multitrigger data sets in which the detector-source orientation and the statistical properties of the data stream change with time, and does not require the assumption that the data is Gaussian. Reconstructing or limiting the energetics of potential gravitational wave emissions associated with quasiperiodic oscillations observed in the x-ray lightcurve tails of soft gamma repeater flares might be an interesting endeavor of the future. Therefore we chose this in a simplified form to illustrate the flow, capabilities, and performance of the method. We investigate performance aspects of a multitrigger based data analysis approach by using $\mathcal{O}(100\mathrm{s})$ long stretches of mock data in coincidence with the times of observed quasiperiodic oscillations, and by using the known sky location of the source. We analytically derive the probability density function of the background distribution and compare to the results obtained by applying the concept to simulated Gaussian noise, as well as off-source playground data collected by the 4-km Hanford detector during LIGO’s fifth science run (S5). We show that the transient glitch rejection and adaptive differential energy comparison methods we apply succeed in rejecting outliers in the fifth science run background data. Finally, we discuss how to extend the method to a network containing multiple detectors, and as an example, tune the method to maximize sensitivity to soft gamma repeater $1806-20$ flare times.

Left-right symmetric models (LRSM) are extensions of the standard model by an enlarged gauge group $SU(2{)}_L\times SU(2{)}_R\times U(1{)}_{B-L,}$ where automatic inclusion of right-handed fermions as $SU(2{)}_R$ doublets guarantees a natural seesaw origin of neutrino masses. Apart from the extended gauge symmetry, LRSM also has a built-in global discrete symmetry, called D-parity, which ensures equal gauge couplings for left and right sectors. Motivated by the fact that global symmetries are expected to be explicitly broken by theories of quantum gravity, here we study the effects of such gravity, or Planck scale physics, on neutrino masses and mixings by introducing explict D-parity breaking, Planck-scale-suppressed, higher-dimensional operators. Although such Planck-scale-suppressd operators have dimensions of at least six in generic LRSM, dimension five operators can also arise in the presence of additional scalar fields, which can be naturally accommodated within $SO(10)$ grand unified theory multiplets. We show that such corrections can give rise to significant changes in the predictions for neutrino mixing parameters compared to the ones predicted by tree-level seesaw formula if the left-right symmetry breaking scale is lower than ${10}^{14}\mathrm{GeV}$.

A determination of the excited energy eigenstates of the nucleon, $s=\frac{1}{2}$, $I=\frac{1}{2}$, $N^{\pm }$, is presented in full QCD using $2+1$ flavor PACS-CS gauge configurations. The correlation-matrix method is used and is built using standard nucleon interpolators employing smearings at the fermion sources and sinks. We develop and demonstrate a new technique that allows the eigenvectors obtained to be utilized to track the propagation of the intrinsic nature of energy states from one quark mass to the next. This approach is particularly useful for larger dimension correlation matrices where more near-degenerate energy states can appear in the spectrum.

We study and constrain the parameter space of the vector color-octet model from the observed data at the Tevatron by studying the top quark pair production and associated observables $A_{\mathrm{FB}}^{t\overline{t}}$ and spin correlation. In particular we study the invariant mass and rapidity dependence of $A_{\mathrm{FB}}^{t\overline{t}}$ at the Tevatron. In addition to the flavor conserving (FC) couplings we extend our study to include the flavor violating (FV) coupling involving the first and third generation quarks for both these processes. In order to ensure that we remain within the constraints imposed by the LHC data, we analyze the charge asymmetry, $p_T$ spectrum and invariant mass in the $t\overline{t}$ production data at the LHC. The constraints from the dijet resonance searches performed by the LHC are also considered. We also explore the contribution of this model to the single top quark production mediated by charged and neutral color-octet vector bosons. FV couplings introduced then induce the same-sign top-pair production process which is analyzed for both the hadron colliders. We have incorporated the effect of finite decay width of color octets on these processes. We find that it is possible to explain the observed $A_{\mathrm{FB}}^{t\overline{t}}$ anomaly in the color-octet vector model without transgressing the production cross sections of all these processes both through FC and FV couplings at the Tevatron. We predict best point sets in the model parameter space for specific choices of color-octet masses corresponding to ${\chi }_{\min }^2$ evaluated using the $m_{t\overline{t}}$ and $|\Delta y|$ spectrum of $A_{\mathrm{FB}}^{t\overline{t}}$ from the observed data set of Run II of the Tevatron at the integrated luminosity $8.7{\mathrm{fb}}^{-1}$. We find that the single top quark production is more sensitive to the FC and FV couplings in comparison to the top-pair production. We provide 95% exclusion contours on the plane of FV chiral couplings from the recent data from Tevatron, CMS and ATLAS corresponding to the nonobservability of large same-sign dilepton events. The four observed point sets are consistent with the cross section, charge asymmetry and spin-correlation measurements for $t\overline{t}$ production and dijet searches at the LHC.

Large-$N_c$ relations among baryonic Isgur-Wise functions appearing at the order of $1/m_Q$ are analyzed. An application to ${\Omega }_b\to {\Omega }_c$ weak decays is given.

We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature. We provide a clean solution to the long standing puzzle about their precise relation, and obtain some universal formulas. We show that the partition function is invariant under the $SL(2,\mathbb{Z})$ duality which exchanges theories at strong coupling with those of weak coupling.

We present a systematic approach to finding Higgs vacuum expectation values, which break a symmetry $G$ to differently embedded isomorphic copies of a subgroup $H\subset G$. We give an explicit formula for recovering each point in the vacuum manifold of a Higgs field which breaks $G\to H$. In particular we systematically identify the vacuum manifold $G/H$ with linear combinations of the vacuum expectation values breaking $G\to H_1\to \cdots \to H_l$. We focus on the most applicable case for current work on grand unified theories in extra-dimensional models and low-energy effective theories for quantum chromodynamics. Here the subgroup, $H$, stabilizes the highest weight of the fundamental representation leading to a simple expression for each element of the vacuum manifold; especially for an adjoint Higgs field. These results are illustrated explicitly for adjoint Higgs fields and clearly linked to the mathematical formalism of Weyl groups. We use the final section to explicitly demonstrate how our work contributes to two contemporary high-energy physics research areas.

Roberge and Weiss showed that for $SU(N)$ gauge theories, phase transitions occur in the presence of an imaginary quark chemical potential. We show that at asymptotically high temperature, where the phase transition is of first order, that even with dynamical quarks ’t Hooft loops of arbitrary $Z(N)$ charge are well defined at the phase boundary. To leading order in weak coupling, the ’t Hooft loop satisfies Casimir scaling in the pure glue theory, but not with quarks. Because the chemical potential is imaginary, typically the interaction measure is negative on one side of the phase transition. Using a matrix model to model the deconfining phase transition, we compute the phase diagram for heavy quarks, in the plane of temperature and imaginary chemical potential. In general we find intersecting lines of first order transitions. Using a modified Polyakov loop which is Roberge-Weiss symmetric, we suggest that the interface tension is related to the ’t Hooft loop only at high temperature, where the imaginary part of this Polyakov loop, and not the real part, is discontinuous across the phase boundary.

The Einstein Telescope (ET) is a proposed future gravitational wave detector. Its design is original, using a triangular orientation of three detectors and a xylophone configuration, splitting each detector into one high-frequency and one low-frequency system. In other aspects the current design retains the dual-recycled Michelson interferometer typical of current detectors, such as Advanced LIGO. In this paper, we investigate the feasibility of replacing the low-frequency part of the ET detectors with a Sagnac interferometer. We show that a Sagnac interferometer, using realistic optical parameters based on the ET design, could provide a similar level of radiation pressure noise suppression without the need for a signal recycling mirror and the extensive filter cavities. We consider the practical issues of a realistic, power-recycled Sagnac, using linear arm cavities and polarizing optics. In particular, we investigate the effects of nonperfect polarizing optics and propose a new method for the generation of a local oscillator field similar to the DC readout scheme of current detectors.

In high statistics observations of $B^o\to J/\psi K^o$ originating from the process ${\rm Y}(4S)\to B^o{\overline{B}}^o$ it should be possible to observe “cascade mixing,” where one mixing particle, the $B^o$, turns into another, the $K^o$. This is possible despite the difficulty that the length of the beam crossing region makes a precise definition of the primary vertex impossible. This difficulty is circumvented by using an “away side” tag to specify the initial time. We review the formalism for describing such processes, and first apply it to simple $B^o$ mixing, noting that it gives a transparent description for $CP$ and $T$ asymmetries. In particular, we show that three different asymmetries of the $CP$ and $T$ type, with neglect of direct $CP$ violation, are given by the same expression. For cascade mixing we present predictions for processes of the type $B_i\to K_j$ via $J/\psi$, where in the limit of no direct $CP$ violation each state $i$ or $j$ is determined by a simple tag. There are 16 such simple measurable processes, involving 10 functions of the two time intervals involved. The coefficients of the functions are different for each of the processes and are given in terms of the mass splitting and the $CP$, $T$ violating parameter of the $B^o$ mass matrix $m_2$. The results presented here are just consequences of the quantum mechanics of particle mixing and do not involve any particular model of $CP$ violation.