We couple $\mathcal{N}=4$ chiral supermultiplet with an auxiliary $\mathcal{N}=4$ fermionic supermutiplet containing on-shell four physical fermions and four auxiliary bosons. The latter ones play the role of isospin variables. We choose the very specific coupling that results in a component action containing only time derivatives of fermionic components presented in the auxiliary supermultiplet, which therefore may be dualized into auxiliary ones. The resulting component action describes the interaction of the chiral supermultiplet with a magnetic field constant on the pseudosphere $SU(1,1)/U(1)$. Then we specify the prepotential of our theory to get, in the bosonic sector, the action for the particle moving over the pseudosphere—Lobachevsky space. We provide also the Hamiltonian formulation of this system and show that the full symmetry group of our system is $SU(1,1)\times U(1)$. The currents forming the $su(1,1)$ algebra are modified, as compared to the bosonic case, by the fermionic and isospin terms, while the additional $u(1)$ current contains only isospin variables. One of the most important features of our construction is the presence in the Hamiltonian and supercharges of all currents of the isospin group $SU(2)$. Despite the fact that two of the $su(2)$ currents $\{T,\overline{T}\}$ enter the Hamiltonian only through the Casimir operator of the $SU(2)$ group, they cannot be dropped out, even after fixing the total isospin of the system, because these currents themselves enter into the supercharges. We also present the Hamiltonian and supercharges describing the motion of a particle over the sphere $S^2$ in the background of a constant magnetic field. In this case the additional isospin currents form the $su(1,1)$ algebra.

Renormalizability of the (minimal) single-fermion QED extension is investigated at all orders of perturbation theory in the framework of algebraic renormalization, a regularization-independent method. Relative to the standard QED, new structures that could lead to gauge anomalies are identified. Nevertheless, even if the anomaly coefficients fail to vanish in the general case, they shall be absent provided we require invariance of the action under $C$ and/or $PT$ transformations. Stability is also verified in this case, hence full renormalizability is attained.

We study acceleration of current-carrying string loops governed by the presence of an outer tension barrier and an inner angular momentum barrier in the field of Schwarzschild-de Sitter black holes. We restrict attention to the axisymmetric motion of string loops with energy high enough, when the string loop can overcome the gravitational attraction and escape to infinity. We demonstrate that string loops can be scattered near the black hole horizon, and the energy of string oscillations can be efficiently converted to the energy of their linear motion. Such a transmutation effect can potentially represent acceleration of jets in active galactic nuclei and microquasars. We give the conditions limiting energy available for conversion onto the jetlike motion. Surprisingly, we are able to show that string loops starting from rest can be accelerated up to velocities $v\sim c$ even in the field of Schwarzschild black holes, if their angular momentum parameter is low enough. Such loops could serve as an explanation of highly relativistic jets observed in some quasars and active galactic nuclei. The cosmic repulsion becomes important behind the so-called static radius where it accelerates the linear motion of the string loops up to velocity $v=c$ that is reached at the cosmic horizon of the Schwarzschild-de Sitter spacetimes independently of the angular momentum parameter of the strings.

We derive the equations of motion, the periastron shift, and the gravitational radiation damping for quasicircular compact binaries in a massive variant of the Brans-Dicke theory of gravity. We also study the Shapiro time delay and the Nordtvedt effect in this theory. By comparing with recent observational data, we put bounds on the two parameters of the theory: the Brans-Dicke coupling parameter ${\omega }_{\mathrm{BD}}$ and the scalar mass $m_s$. We find that the most stringent bounds come from Cassini measurements of the Shapiro time delay in the Solar System that yield a lower bound ${\omega }_{\mathrm{BD}}>40000$ for scalar masses $m_s<2.5\times {10}^{-20}\mathrm{eV}$ [or Compton wavelengths ${\lambda }_s=h/(m_{s}c)>5\times {10}^{10}\mathrm{km}$], to 95% confidence. In comparison, observations of the Nordtvedt effect using lunar laser ranging experiments yield ${\omega }_{\mathrm{BD}}>1000$ for $m_s<2.5\times {10}^{-20}\mathrm{eV}$. Observations of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR $\mathrm{J}1012+5307$ yield ${\omega }_{\mathrm{BD}}>1250$ for $m_s<{10}^{-20}\mathrm{eV}$ (${\lambda }_s>1.2\times {10}^{11}\mathrm{km}$). A first estimate suggests that bounds comparable to the Shapiro time delay may come from observations of radiation damping in the eccentric white dwarf-neutron star binary PSR $\mathrm{J}1141-6545$, but a quantitative prediction requires the extension of our work to eccentric orbits.

We present a new formulation of the Einstein equations based on a conformal and traceless decomposition of the covariant form of the Z4 system. This formulation combines the advantages of a conformal decomposition, such as the one used in the BSSNOK formulation (i.e. well-tested hyperbolic gauges, no need for excision, robustness to imperfect boundary conditions) with the advantages of a constraint-damped formulation, such as the generalized harmonic one (i.e. exponential decay of constraint violations when these are produced). We validate the new set of equations through standard tests and by evolving binary black hole systems. Overall, the new conformal formulation leads to a better behavior of the constraint equations and a rapid suppression of the violations when they occur. The changes necessary to implement the new conformal formulation in standard BSSNOK codes are very small as are the additional computational costs.

First laws of black hole mechanics, or thermodynamics, come in a variety of different forms. In this paper, from a purely post-Newtonian (PN) analysis, we obtain a first law for binary systems of point masses moving along an exactly circular orbit. Our calculation is valid through 3PN order and includes, in addition, the contributions of logarithmic terms at 4PN and 5PN orders. This first law of binary point-particle mechanics is then derived from first principles in general relativity, and analogies are drawn with the single and binary black hole cases. Some consequences of the first law are explored for PN spacetimes. As one such consequence, a simple relation between the PN binding energy of the binary system and Detweiler’s redshift observable is established. Through it, we are able to determine with high precision the numerical values of some previously unknown high-order PN coefficients in the circular-orbit binding energy. Finally, we propose new gauge-invariant notions for the energy and angular momentum of a particle in a binary system.

We investigate the vacuum $pp$-wave and Aichelburg-Sexl-type solutions in $f(R)$ and the modified Gauss-Bonnet theories of gravity with both minimal and nonminimal couplings between matter and geometry. In each case, we obtain the necessary condition for the theory to admit the solution and examine it for several specific models. We show that the wave profiles are the same or proportional to the general relativistic one.

One component of a massive black hole binary might capture a small third body, and then a hierarchical, inclined triple system would be formed. With the post-Newtonian approximation including radiation reaction, we analyzed the evolution of the triple initially with small eccentricities. We found that an essentially new resonant relation could arise in the triple system. Here relativistic effects are crucial. Relativistic resonances, including the new one, stably work even for an outer massive black hole binary of comparable masses, and significantly change the orbit of the inner small body.

We consider a cosmology in which the final stage of the Universe is neither accelerating nor decelerating, but approaches an asymptotic state where the scale factor becomes a constant value. In order to achieve this, we first bring in a scale factor with the desired property and then determine the details of the energy contents as a result of the cosmological evolution equations. We show that such a scenario can be realized if we introduce a generalized quintom model which consists of a scalar field and a phantom with a negative cosmological constant term. The standard cold dark matter with $w_m=0$ is also introduced. This is possible basically due to the balance between the matter and the negative cosmological constant which tend to attract and scalar field and phantom which repel in the asymptotic region. The stability analysis shows that this asymptotic solution is classically stable.

The RICE experiment seeks observation of ultra-high energy (UHE; $E_{\nu }>{10}^{17}\mathrm{eV}$) neutrinos interacting in Antarctic ice, by measurement of the radio frequency (RF) Cherenkov radiation resulting from the collision of a neutrino with an ice molecule. RICE was initiated in 1999 as a first-generation prototype for an eventual, large-scale in-ice UHE neutrino detector. Herein, we present updated limits on the diffuse UHE neutrino flux, based on 12 years of data taken between 1999 and 2010. We find no convincing neutrino candidates, resulting in 95% confidence-level model-dependent limits on the flux $E_{\nu }^{2}d\varphi /d{E}_{\nu }<0.5\times {10}^{-6}\mathrm{GeV}/({\mathrm{cm}}^2\mathrm{s}\mathrm{\text{−}}\mathrm{sr})$ in the energy range ${10}^{17}<E_{\nu }<{10}^{20}\mathrm{eV}$, or approximately a twofold improvement over our previously published results. Recently, the focus of RICE science has shifted to studies of radio frequency ice properties as the RICE experimental hardware has been absorbed into a new experimental initiative (the Askaryan Radio Array, or “ARA”) at the south pole. ARA seeks to improve on the RICE sensitivity by approximately 2 orders of magnitude by 2017 and thereby establish the cosmogenic neutrino flux. As detailed herein, RICE studies of Antarctic ice demonstrate that both birefringence and internal layer RF scattering result in no significant loss of ARA neutrino sensitivity, and, for the first time, verify in situ the decrease in attenuation length with depth into the Antarctic ice sheet.

We discuss techniques for evaluating sea quark contributions to hadronic form factors on the lattice and apply these to an exploratory calculation of the strange electromagnetic, axial, and scalar form factors of the nucleon. We employ the Wilson gauge and fermion actions on an anisotropic ${24}^3\times 64$ lattice, probing a range of momentum transfer with $Q^2<1{\mathrm{GeV}}^2$. The strange electric and magnetic form factors, $G_E^s(Q^2)$ and $G_M^s(Q^2)$, are found to be small and consistent with zero within the statistics of our calculation. The lattice data favor a small negative value for the strange axial form factor $G_A^s(Q^2)$ and exhibit a strong signal for the bare strange scalar matrix element $⟨N|\overline{s}s|N{⟩}_0$. We discuss the unique systematic uncertainties affecting the latter quantity relative to the continuum, as well as prospects for improving future determinations with Wilson-like fermions.

We present the first results on the Dalitz-plot structure and improved measurements of the time-dependent $CP$-violation parameters of the process $B^0\to K_S^0{K}_S^0{K}_S^0$ obtained using $468\times {10}^{6}B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC. The Dalitz-plot structure is probed by a time-integrated amplitude analysis that does not distinguish between $B^0$and ${\overline{B}}^0$ decays. We measure the total inclusive branching fraction $\mathcal{B}(B^0\to K_S^0{K}_S^0{K}_S^0)=(6.19\pm 0.48\pm 0.15\pm 0.12)\times {10}^{-6}$, where the first uncertainty is statistical, the second is systematic, and the third represents the Dalitz-plot signal model dependence. We also observe evidence for the intermediate resonant states $f_0(980)$, $f_0(1710)$, and $f_2(2010)$. Their respective product branching fractions are measured to be $({2.70}_{-1.19}^{+1.25}\pm 0.36\pm 1.17)\times {10}^{-6}$, $({0.50}_{-0.24}^{+0.46}\pm 0.04\pm 0.10)\times {10}^{-6}$, and $({0.54}_{-0.20}^{+0.21}\pm 0.03\pm 0.52)\times {10}^{-6}$. Additionally, we determine the mixing-induced $CP$-violation parameters to be $\mathcal{S}=-{0.94}_{-0.21}^{+0.24}\pm 0.06$ and $\mathcal{C}=-0.17\pm 0.18\pm 0.04$, where the first uncertainty is statistical and the second is systematic. These values are in agreement with the standard model expectation. For the first time, we report evidence of $CP$ violation in $B^0\to K_S^0{K}_S^0{K}_S^0$ decays; $CP$ conservation is excluded at 3.8 standard deviations including systematic uncertainties.

A beautiful understanding of the smallness of the neutrino masses may be obtained via the seesaw mechanism, whereby one takes advantage of the key qualitative distinction between the neutrinos and the other fermions: right-handed neutrinos are gauge singlets, and may therefore have large Majorana masses. The standard seesaw mechanism, however, does not address the apparent lack of hierarchy in the neutrino masses compared to the quarks and charged leptons, nor the large leptonic mixing angles compared to the small angles of the Cabibbo-Kobayashi-Maskawa matrix. In this paper, we will show that the singlet nature of the right-handed neutrinos may be taken advantage of in one further way in order to solve these remaining problems: Unlike particles with gauge interactions, whose numbers are constrained by anomaly cancellation, the number of gauge singlet particles is essentially undetermined. If large numbers of gauge singlet fermions are present at high energies—as is suggested, for example, by various string constructions—then the effective low-energy neutrino mass matrix may be determined as a sum over many distinct Yukawa couplings, with the largest ones being the most important. This can reduce hierarchy, and lead to large mixing angles. Assuming a statistical distribution of fundamental parameters, we will show that this scenario leads to a good fit to low-energy phenomenology, with only a few qualitative assumptions guided by the known quark and lepton masses. The scenario leads to predictions of a normal hierarchy for the neutrino masses, and a value for the $|m_{\mathrm{ee}}|$ mass matrix element of about 1–6 meV.

The type-I seesaw Lagrangian yields a nongeneric set of active-sterile oscillation parameters—the neutrino mass eigenvalues and the physical elements of the full mixing matrix are entwined. For this reason one is able to, in principle, test the model by performing enough measurements which are sensitive to neutrino masses and lepton mixing. We point out that for light enough right-handed neutrino masses—less than 10 eV—next-generation short-baseline neutrino oscillation experiments may be able to unambiguously rule out (or “rule in”) the low-energy seesaw as the Lagrangian that describes neutrino masses. These types of searches are already under consideration in order to address the many anomalies from accelerator neutrino experiments (LSND, MiniBooNe), reactor neutrino experiments (the “reactor anomaly”), and others. In order to test the low-energy seesaw, it is crucial to explore different oscillation channels, including ${\nu }_e$ and ${\nu }_{\mu }$ disappearance and ${\nu }_{\mu }\leftrightarrow {\nu }_{\tau }$ appearance.

Three-jet production in deep inelastic $ep$ scattering and photoproduction was investigated with the ZEUS detector at HERA using an integrated luminosity of up to $127{\mathrm{pb}}^{-1}$. Measurements of differential cross sections are presented as functions of angular correlations between the three jets in the final state and the proton-beam direction. These correlations provide a stringent test of perturbative QCD and show sensitivity to the contributions from different color configurations. Fixed-order perturbative calculations assuming the values of the color factors $C_F$, $C_A$, and $T_F$ as derived from a variety of gauge groups were compared to the measurements to study the underlying gauge group symmetry. The measured angular correlations in the deep inelastic $ep$ scattering and photoproduction regimes are consistent with the admixture of color configurations as predicted by SU(3) and disfavour other symmetry groups, such as $\mathrm{SU}(N)$ in the limit of large $N$.

The purpose of this paper is to perform a quantitative check of gauge theory–gravity duality in a nonconformal, nonsupersymmetric context. In order to do so we define $k_5$, an object extracted from the Wilson loop, that plays the role of Coulomb’s constant for $SU(N)$ gauge theories in five dimensions, and we argue that one of its virtues is that it could be minimally sensitive to $N$. This allows us to compute $k_5$ on one hand from the gravitational backreation of a large number $N$ of $D4$-branes, and on the other from a lattice mean-field expansion for $N=2$. We find a 2% numerical agreement between the two approaches.

We consider the phenomenological consequences of fixing compactification moduli. In the simplest Kachru-Kallosh-Linde-Trivedi constructions, stabilization of internal dimensions is rather soft: weak scale masses for moduli are generated, and are of order $m_{\sigma }\sim m_{3/2}$. As a consequence one obtains a pattern of soft supersymmetry breaking masses found in gravity and/or anomaly mediated supersymmetry breaking (AMSB) models. These models may lead to destabilization of internal dimensions in the early universe, unless the Hubble constant during inflation is very small. Fortunately, strong stabilization of compactified dimensions can be achieved by a proper choice of the superpotential (e.g., in the Kallosh-Linde model with a racetrack superpotential). This allows for a solution of the cosmological moduli problem and for a successful implementation of inflation in supergravity. We show that strong moduli stabilization leads to a very distinct pattern of soft supersymmetry breaking masses. In general, we find that soft scalar masses remain of order the gravitino mass, while gaugino masses nearly vanish at the tree level; i.e., they are of order $m_{3/2}^2/m_{\sigma }$. Radiative corrections generate contributions to gaugino masses reminiscent of AMSB models and a decoupled spectrum of scalars reminiscent of split supersymmetry. This requires a relatively large gravitino mass [$\sim \mathcal{O}(100)\mathrm{TeV}$], resolving the cosmological gravitino problem and problems with tachyonic staus in AMSB models.

We determine the phase structure of an $SU(2)$ gauge theory with an adjoint scalar on $R^3\times S^1$ using semiclassical methods. There are two global symmetries: a $Z(2{)}_H$ symmetry associated with the Higgs field and a $Z(2{)}_C$ center symmetry associated with the Polyakov loop in the compact direction. The order of the deconfining phase transition can be either second-order or first-order for $SU(2)$, depending on the deformation used. After finding order parameters for the global symmetries, we show that there are four distinct phases: a deconfined phase, a confined phase, a Higgs phase, and a mixed confined phase. The mixed confined phase occurs where one might expect a phase in which there is both confinement and the Higgs mechanism, but the behavior of the order parameters distinguishes the two phases. In the mixed confined phase, the $Z(2{)}_C\times Z(2{)}_H$ global symmetry breaks spontaneously to a $Z(2)$ subgroup that acts nontrivially on both the scalar field and the Polyakov loop. We find explicitly the BPS and KK monopole solutions of the Euclidean field equations in the BPS limit; these monopoles are extensions of similar pure gauge theory solutions, where they are constituents of instantons. In the mixed phase, a linear combination of the Higgs field $\varphi$ and $A_4$, the component of the gauge field in the compact direction, enters into the monopole solutions. In all four phases, Wilson loops orthogonal to the compact direction are expected to show area-law behavior. We show that this confining behavior can be attributed to a dilute monopole gas in a broad region that includes portions of all four phases. The dilute monopole gas picture breaks down when the action of a BPS monopole is zero. A duality argument similar to that applied recently [40] to the Seiberg-Witten model on $R^3\times S^1$ shows that the monopole gas picture, arrived at using Euclidean instanton methods, can be interpreted as a gas of finite-energy dyons.

We develop a unified formalism for describing the interaction of gravitational waves with matter that clearly separates the effects of general relativity from those due to interactions in the matter. Using it, we derive a general expression for the dispersion of gravitational waves in matter in terms of correlation functions for the matter in flat spacetime. The self energy of a gravitational wave is shown to have contributions analogous to the paramagnetic and diamagnetic contributions to the self energy of an electromagnetic wave. We apply the formalism to some simple systems: free particles, an interacting scalar field, and a fermionic superfluid.

The constraints on the asymptotic behavior of the conformal factor and conformal extrinsic curvature imposed by the initial value equations of general relativity on constant mean extrinsic curvature (CMC) hypersurfaces are analyzed in detail. We derive explicit formulas for the Bondi-Sachs energy and momentum in terms of coefficients of asymptotic expansions on CMC hypersurfaces near future null infinity. Precise numerical results for the Bondi-Sachs energy, momentum, and angular momentum are used to interpret physically Bowen-York initial data on conformally flat CMC hypersurfaces similar to that calculated earlier by Buchman et al. [L. T. Buchman, H. P. Pfeiffer, and J. M. Bardeen, Phys. Rev. D 80, 084024-1 (2009).].