There is considerable evidence, based on large $N_c$ chiral dynamics, holographic QCD, and Monte Carlo studies, that the QCD vacuum is permeated by discrete quasivacua separated by domain walls across which the local value of the topological $\theta$ parameter jumps by $\pm 2\pi$. This scenario is realized in a 2D U(1) gauge theory, the $C{P}^{N-1}$ sigma model, where a pointlike charge is a domain wall, and $\theta$ describes the background electric flux and the polarization of charged pairs in the vacuum. The transition between discrete $\theta$ vacua occurs via the transport of integer units of charge between the two spatial boundaries of the domain. We show that this screening process, and the role of $\theta$ as an order parameter describing electric polarization, are naturally formulated in terms of Bloch wave eigenstates of the Dirac Hamiltonian in the background gauge field. This formulation is similar to the Berry phase description of electric polarization and quantized charge transport in topological insulators. The Bloch waves are quasiperiodic superpositions of localized Dirac zero modes and the charge transport takes place coherently via topological charge-induced spectral flow. The adiabatic spectral parameter becomes the Bloch wave momentum, which defines a Berry connection around the Brillouin zone of the zero mode band. It describes the local polarization of vacuum pairs, analogous to its role in topological insulator theory. In 4D Yang-Mills theory, the $\theta$ domain walls are $2+1$-dimensional Chern-Simons membranes, and the $\theta$ parameter describes the local polarization of brane-antibrane pairs. The topological description of polarization in 2D U(1) gauge theory generalizes to membrane polarization in 4D QCD by exploiting a relationship between the Berry connection and the gauge cohomology structure encoded in the descent equations of 4D Yang-Mills theory.

We introduce a new operator in loop quantum gravity—the 3D curvature operator—related to the three-dimensional scalar curvature. The construction is based on Regge calculus. We define this operator starting from the classical expression of the Regge curvature, we derive its properties and discuss some explicit checks of the semiclassical limit.

A manifestly covariant equation is derived to describe the second-order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski spacetime and introduces a framework for studying in a precise manner membrane behavior near the black hole horizon and on the other hand introduces a more general framework for examining the stability of topological defects in curved spacetimes.

We present a model for the spine of relativistic Magnetohydrodynamics outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semianalytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.

We compute the electromagnetic self-force acting on a charged particle held in place at a fixed position $r$ outside a five-dimensional black hole described by the Schwarzschild-Tangherlini metric. Using a spherical-harmonic decomposition of the electrostatic potential and a regularization prescription based on the Hadamard Green’s function, we express the self-force as a convergent mode sum. The self-force is first evaluated numerically, and next presented as an analytical expansion in powers of $R/r$, with $R$ denoting the event-horizon radius. The power series is then summed to yield a closed-form expression. Unlike its four-dimensional version, the self-force features a dependence on a regularization parameter $s$ that can be interpreted as the particle’s radius. The self-force is repulsive at large distances, and its behavior is related to a model according to which the force results from a gravitational interaction between the black hole and the distribution of electrostatic field energy attached to the particle. The model, however, is shown to become inadequate as $r$ becomes comparable to $R$, where the self-force changes sign and becomes attractive. We also calculate the self-force acting on a particle with a scalar charge, which we find to be everywhere attractive. This is to be contrasted with its four-dimensional counterpart, which vanishes at any $r$.

Astrophysical charge-free black holes are known to satisfy no-hair relations through which all multipole moments can be specified in terms of just their mass and spin angular momentum. We here investigate the possible existence of no-hair-like relations among multipole moments for neutron stars and quark stars that are independent of their equation of state. We calculate the multipole moments of these stars up to hexadecapole order by constructing uniformly rotating and unmagnetized stellar solutions to the Einstein equations. For slowly rotating stars, we construct stellar solutions to quartic order in spin in a slow-rotation expansion, while for rapidly rotating stars, we solve the Einstein equations numerically with the LORENE and RNS codes. We find that the multipole moments extracted from these numerical solutions are consistent with each other and agree with the quartic-order slow-rotation approximation for spin frequencies below roughly 500 Hz. We also confirm that the current dipole is related to the mass quadrupole in an approximately equation-of-state-independent fashion, which does not break for rapidly rotating neutron stars or quark stars. We further find that the current-octupole and the mass-hexadecapole moments are related to the mass quadrupole in an approximately equation-of-state-independent way to roughly $\mathcal{O}(10\%)$, worsening in the hexadecapole case. All of our findings are in good agreement with previous work that considered stellar solutions to leading order in a weak-field, Newtonian expansion. In fact, the hexadecapole-quadrupole relation agrees with the Newtonian one quite well even in moderately relativistic regimes. The quartic in spin, slowly rotating solutions found here allows us to estimate the systematic errors in the measurement of the neutron star’s mass and radius with future x-ray observations, such as Neutron star Interior Composition ExploreR (NICER) and Large Observatory for X-ray Timing (LOFT). We find that the effect of these quartic-in-spin terms on the quadrupole and hexadecapole moments and stellar eccentricity may dominate the error budget for very rapidly rotating neutron stars. The new universal relations found here should help to reduce such systematic errors.

In this paper we elucidate some of the effects of the quartic quasitopological term for Lifshitz-symmetric black holes. The field equations of this theory are difficult to solve exactly; here we use numerical solutions both to verify previous exact solutions for quartic quasitopological anti–de Sitter black holes as well as to examine new quasitopological Lifshitz-symmetric black hole solutions, in order to determine the effect of the quartic coupling parameter on the black hole’s thermodynamic behavior. We find that the quartic parameter controls solutions very similarly to the cubic parameter, allowing for the construction of a theory with another free parameter which may find meaning in the phase transition behavior of a gauge/gravity context.

This paper reports on an unmodeled, all-sky search for gravitational waves from merging intermediate mass black hole binaries (IMBHB). The search was performed on data from the second joint science run of the LIGO and Virgo detectors (July 2009–October 2010) and was sensitive to IMBHBs with a range up to $\sim 200\mathrm{Mpc}$, averaged over the possible sky positions and inclinations of the binaries with respect to the line of sight. No significant candidate was found. Upper limits on the coalescence-rate density of nonspinning IMBHBs with total masses between 100 and $450{\mathrm{M}}_{\odot }$ and mass ratios between 0.25 and 1 were placed by combining this analysis with an analogous search performed on data from the first LIGO-Virgo joint science run (November 2005–October 2007). The most stringent limit was set for systems consisting of two $88{\mathrm{M}}_{\odot }$ black holes and is equal to $0.12{\mathrm{Mpc}}^{-3}{\mathrm{Myr}}^{-1}$ at the 90% confidence level. This paper also presents the first estimate, for the case of an unmodeled analysis, of the impact on the search range of IMBHB spin configurations: the visible volume for IMBHBs with nonspinning components is roughly doubled for a population of IMBHBs with spins aligned with the binary’s orbital angular momentum and uniformly distributed in the dimensionless spin parameter up to 0.8, whereas an analogous population with antialigned spins decreases the visible volume by $\sim 20\%$.

We investigate the charged-neutral difference in the pion self-energy at finite temperature $T$. Within chiral perturbation theory (ChPT) we extend a previous analysis performed in the chiral and soft pion limits. Our analysis with physical pion masses leads to additional non-negligible contributions for temperatures typical of a meson gas, including a momentum-dependent function for the self-energy. In addition, a nonzero imaginary part arises to leading order, which we define consistently in the Coulomb gauge and comes from an infrared enhanced contribution due to thermal bath photons. For distributions typical of a heavy-ion meson gas, the charged and neutral pion masses and their difference depend on temperature through slowly increasing functions. Chiral symmetry restoration turns out to be ultimately responsible for keeping the charged-neutral mass difference smooth and compatible with the observed charged and neutral pion spectra. We study also phenomenological effects related to the thermal electromagnetic damping, which gives rise to corrections for transport coefficients and distinguishes between neutral and charged mean free times. An important part of the analysis is the connection with chiral symmetry restoration through the relation of the pion mass difference with the vector-axial spectral function difference, which holds at $T=0$ due to a sum rule in the chiral and soft pion limits. We analyze the modifications of that sum rule including nonzero pion masses and temperature, up to $\mathcal{O}(T^2)\sim \mathcal{O}(M_{\pi }^2)$. Both effects produce terms making the pion mass difference grow against chiral-restoring decreasing contributions. Finally, we analyze the corrections to the previous ChPT and sum rule results within the resonance saturation framework at finite temperature, including explicitly $\rho$ and $a_1$ exchanges. Our results show that the ChPT result is robust at low and intermediate temperatures, the leading resonance corrections within this framework being $\mathcal{O}(T^2{M}_{\pi }^2/M_R^2)$ with $M_R$ the involved resonance masses.

The discovery of a 126 GeV Higgs-like scalar at the LHC along with the nonobservation of the supersymmetric particles has in turn led to constraining various supersymmetric models through the Higgs data. We here consider the case of both the minimal supersymmetric standard model (MSSM) as well its extension containing an additional chiral singlet superfield, the next-to-minimal or nonminimal supersymmetric standard model (NMSSM). A lot of work has been done in the context of the lightest scalar of these models being identified as the 126 GeV state discovered at the LHC. We here, however, concentrate on the case where we identify the second lightest Higgs boson as the 126 GeV state discovered at the CERN LHC and consider the invisible decays of the low mass Higgs bosons in both the MSSM and NMSSM. In the case of the MSSM we consider $H\approx 126\mathrm{GeV}$ and $h\approx 98\mathrm{GeV}$, known as the nondecoupling regime, whereas in the case of the NMSSM $h_2\approx 126\mathrm{GeV}$, with $m_{h_1}$ and $m_{a_1}$ varying depending on the parameter space. We find that, in the case of the MSSM with universal boundary conditions at the grand unified theory (GUT) scale, it is not possible to have light neutralinos leading to the decay channel $H\to {\tilde{\chi }}_1^0{\tilde{\chi }}_1^0$. The invisible decay mode is allowed in the case of certain $SO(10)$ and $E_6$ grand unified models with large representations and nonuniversal gaugino masses at the GUT scale. In the case of the NMSSM, for the parameter space considered it is possible to have the invisible decay channel with universal gaugino masses at the GUT scale. We furthermore consider the most general case, with $M_1$ and $M_2$ as independent parameters for both the MSSM and NMSSM. We isolate the regions in parameter space in both cases where the second lightest Higgs boson has a mass of 126 GeV and then concentrate on the invisible decay of Higgs bosons to lighter neutralinos. The other nonstandard decay mode of the Higgs boson is also considered in detail. The invisible Higgs branching ratio being constrained by the LHC results, we find that, in this case with the second lightest Higgs boson being the 126 GeV state, more data from the LHC are required to constrain the neutralino parameter space, compared to the case when the lightest Higgs boson is the 126 GeV state.

We discuss the Higgs inflation scenario with singlet scalar dark matter and a right-handed neutrino. The singlet scalar and the right-handed neutrino play crucial roles for realizing a suitable plateau of Higgs potential with the center value of the top mass of Tevatron and LHC measurements. This Higgs inflation scenario predicts about a 1 TeV scalar dark matter and an $\mathcal{O}(10^{14})\mathrm{GeV}$ right-handed neutrino by use of a 125.6 GeV Higgs mass, 173.34 GeV top mass, and a nonminimal gravity coupling $\xi \simeq 10.1$. This inflation model is consistent with the recent result of the tensor-to-scalar ratio $r=0.20_{-0.05}^{+0.07}$ by the BICEP2 Collaboration.

In two-Higgs doublet extensions of the Standard Model, flavor-changing neutral current constraints can be addressed by introducing a $U(1{)}^{\prime }$ gauge symmetry, under which the Higgs doublets carry different charges. That scenario implies the presence of a $H^{\pm }{W}^{\mp }{Z}^{\prime }$ vertex at tree level. For the light “dark” $Z$ model ($Z^{\prime }=Z_d$) with $m_{Z_d}<10\mathrm{GeV}$, such a coupling leads to the dominant decay mode $H^{\pm }\to W^{\pm }+Z_d$ (for $m_{H^{\pm }}\lesssim 175\mathrm{GeV}$), rather than the usual type I model decay $H^{\pm }\to {\tau }^{\pm }\nu$, for a broad range of parameters. We find that current analyses do not place significant bounds on this scenario. Over much of the parameter space considered, the decay of a pair-produced $t$ ($\overline{t}$) into $H^{+}b$ ($H^{-}\overline{b}$) provides the dominant $H^{\pm }$ production. Analysis of available LHC data can likely cover significant ranges of our parameters, if $Z_d\to {\mu }^{+}{\mu }^{-}$ has a branching ratio of $\sim 20\%$. If the $Z_d$ decays mainly invisibly then probing the entire relevant parameter space would likely require additional data from future LHC runs. We briefly discuss the phenomenology for $m_{H^{\pm }}\gtrsim 175\mathrm{GeV}$.

We present the calculations for the same-sign $T$-odd mirror quark pair production of the first two generations in the littlest Higgs model with $T$ parity (LHT) at the $\sqrt{s}=14\mathrm{TeV}$ LHC up to the QCD next-to-leading order (NLO) including the subsequent decays of the $T$-odd mirror quarks. The uncertainties from the factorization/renormalization scale and parton distribution functions are discussed. Our numerical results show that the parton distribution function uncertainty of the NLO QCD corrected cross section for the same-sign $T$-odd mirror quark pair production of the first two generations is comparable with the scale uncertainty, and the combined uncertainty at the QCD NLO is much smaller than that at the LO with the factorization/renormalization scale $\mu$ in the range of $[{\mu }_0/4,4{\mu }_0]$. We also study the dependence of the total cross section on the LHT parameters, and provide the transverse momentum, rapidity, invariant mass and $H_T$ distributions of final products.

We report the results of a search for the neutrinoless double-$\beta$ decay ($0\nu \beta \beta$) of ${}^{100}\mathrm{Mo}$, using the NEMO-3 detector to reconstruct the full topology of the final state events. With an exposure of $34.7\mathrm{kg}·\mathrm{y}$, no evidence for the $0\nu \beta \beta$ signal has been found, yielding a limit for the light Majorana neutrino mass mechanism of $T_{1/2}(0\nu \beta \beta )>1.1\times {10}^{24}$ years (90% C.L.) once both statistical and systematic uncertainties are taken into account. Depending on the nuclear matrix elements this corresponds to an upper limit on the Majorana effective neutrino mass of $⟨m_{\nu }⟩<0.3–0.9\mathrm{eV}$ (90% C.L.). Constraints on other lepton number violating mechanisms of $0\nu \beta \beta$ decays are also given. Searching for high-energy double electron events in all suitable sources of the detector, no event in the energy region [3.2–10] MeV is observed for an exposure of $47\mathrm{kg}·\mathrm{y}$.

We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, $VV\to VV$. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero- through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals and show how discrete symmetries of these varieties largely determine the constraints.

We study kink scattering processes in the $(1+1)$-dimensional ${\phi }^6$ model in the framework of the collective coordinate approximation. We find critical values of the initial velocities of the colliding kinks. These critical velocities distinguish different regimes of collisions. The exact equation of motion for the ${\phi }^6$ model is also solved numerically with the same initial conditions. We discuss advantages and disadvantages of the collective coordinate approximation, and also outline its applicability limits. Resonance phenomena and the so-called escape windows are also observed in the kink collisions.

A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar and formulate it directly in terms of the deformed curvature of the body’s surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.

We show that the Ashtekar-Magnon-Das mass and other conserved quantities are equivalent to the Kounterterm charges in the asymptotically anti-de Sitter space-times that satisfy the Einstein equations, if we assume the same asymptotic falloff behavior of the Weyl tensor as considered by Ashtekar, Magnon, and Das. This, therefore, implies that, in all dimensions, the conformal mass can be directly derived from the bulk action and the boundary terms, which are written in terms of the extrinsic curvature.

We study phenomenological aspects of the bino-wino coannihilation scenario in high-scale supersymmetry (SUSY)-breaking models. High-scale SUSY-breaking scenarios are considered to be a promising possibility after the discovery of the Higgs boson with a mass around 126 GeV. In this paper, we discuss the bino lightest supersymmetric particle (LSP), accompanied by the (at most) around 30 GeV heavier wino. With suitable mass splitting between the bino and the wino, the bino LSP has the correct relic abundance of dark matter. For a smaller mass splitting, the late-time decay of the gravitino can provide the correct abundance of bino dark matter. It is extremely challenging to find signals from the bino dark matter in direct and indirect detections. By utilizing multijets plus missing transverse momentum events at the LHC, we can constrain the gluino mass and thus probe the bino-wino coannihilation scenario indirectly. The collider experiment, however, cannot search the bino dark matter directly. In this paper, we suggest the direct probe of the bino dark matter. We show that the bino dark matter leaves imprints on the small-scale matter power spectrum when the bino dark matter is produced by the decay of the gravitino. The nonthermal bino dark matter behaves as mixed ($\mathrm{cold}+\mathrm{warm}$) dark matter.

The IceCube experiment has recently reported the first observation of high-energy cosmic neutrinos. Their origin is still unknown. In this paper, we investigate the possibility that they originate in active galaxies. We show that hadronic interactions (pp) in the generally less powerful, more frequent, FR-I radio galaxies are one of the candidate source classes being able to accommodate the observation while the more powerful, less frequent, class of FR-II radio galaxies has too low of a column depths to explain the signal.