Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect to exchange of Dirac indices. Nonlocal baryon operators are formulated in a second step as direct products of the spinor structures of smeared, local operators together with gauge-covariant lattice displacements of one or more of the smeared quark fields. Linear combinations of direct products of spinorial and spatial irreducible representations are then formed with appropriate Clebsch-Gordan coefficients of the octahedral group. The construction attempts to maintain maximal overlap with the continuum $SU(2)$ group in order to provide a physically interpretable basis. Nonlocal operators provide direct couplings to states that have nonzero orbital angular momentum.

We analyze topological solitons in the noncommutative plane by taking a concrete instance of the quantum Hall system with the $SU(N)$ symmetry, where a soliton is identified with a Skyrmion. It is shown that a topological soliton induces an excitation of the electron number density from the ground-state value around it. When a judicious choice of the topological charge density $J_0(\mathbf{x})$ is made, it acquires a physical reality as the electron density excitation $\Delta {\rho }^{\mathrm{cl}}(\mathbf{x})$ around a topological soliton, $\Delta {\rho }^{\mathrm{cl}}(\mathbf{x})=-J_0(\mathbf{x})$. Hence a noncommutative soliton carries necessarily the electric charge proportional to its topological charge. A field-theoretical state is constructed for a soliton state irrespectively of the Hamiltonian. In general, it involves an infinitely many parameters. They are fixed by minimizing its energy once the Hamiltonian is chosen. We study explicitly the cases where the system is governed by the hard-core interaction and by the noncommutative $C{P}^{N-1}$ model, where all these parameters are determined analytically and the soliton excitation energy is obtained.

We compute the leading-color (planar) three-loop four-point amplitude of $N=4$ supersymmetric Yang-Mills theory in $4-2ϵ$ dimensions, as a Laurent expansion about $ϵ=0$ including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar $N=4$ amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated Ansatz for the maximally helicity-violating $n$-point amplitudes to all loop orders. The $1/{ϵ}^2$ pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in $N=4$ supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.

We investigate the decays of ${\chi }_{c0,2}$ into vector meson pairs ($VV$), pseudoscalar pairs ($PP$), and scalar pairs ($SS$) in a general factorization scheme. The purpose is to clarify the role played by the OZI-rule violations and SU(3) flavour breakings in the decay transitions, and their correlations with the final-state meson wavefunctions. For ${\chi }_{c0,2}\to VV$ and $PP$, we obtain an overall self-contained description of the experimental data. Applying this factorization to ${\chi }_{c0}\to f_0^i{f}_0^j$, where $i,j=1,2,3$ denotes $f_0(1710)$, $f_0(1500)$ and $f_0(1370)$, respectively, we find that specific patterns will arise from the model predictions for the decay branching ratio magnitudes, and useful information about the structure of those three scalars can be abstracted.

A search for mixing in the neutral $D$ meson system has been performed using semileptonic $D^0\to K^{(*)-}{e}^{+}\nu$ decays. Neutral $D$ mesons from $D^{*+}\to D^0{\pi }^{+}$ decays are used; the flavor at production is tagged by the charge of the slow pion. The measurement is performed using $253{\mathrm{fb}}^{-1}$ of data recorded by the Belle detector. From the yield of right-sign and wrong-sign decays arising from nonmixed and mixed events, respectively, we estimate the upper limit of the time-integrated mixing rate to be $r_D<1.0\times {10}^{-3}$ at $90\%$ C.L.

Based on new developments in the understanding of supernovae (SNe) as gravitational-wave (GW) sources we estimate the GW background from all cosmic SNe. For a broad range of frequencies around 1 Hz, this background is crudely comparable to the GW background expected from standard inflationary models. While our estimate remains uncertain within several orders of magnitude, the SN GW background may become detectable by second-generation space-based interferometers such as the proposed Big Bang Observatory (BBO). By the same token, the SN GWs may become a foreground for searches of the inflationary GWs, in particular, for sub-Hz frequencies where the SN background is Gaussian and where the BBO will be most sensitive. SN simulations lasting far beyond the usual cutoff of about 1 s are needed for more robust predictions in the sub-Hz frequency band. An even larger GW background can arise from a hypothetical early population of massive stars, although their GW source strength as well as their abundance are currently poorly understood.

We investigate the recent suggestions by Barausse et al. and Kolb et al. that the acceleration of the universe could be explained by large superhorizon fluctuations generated by inflation. We show that no acceleration can be produced by this mechanism. We begin by showing how the application of Raychaudhuri equation to inhomogeneous cosmologies results in several “no go” theorems for accelerated expansion. Next we derive an exact solution for a specific case of initial perturbations, for which application of the Kolb et al. expressions leads to an acceleration, while the exact solution reveals that no acceleration is present. We show that the discrepancy can be traced to higher-order terms that were dropped in the Kolb et al. analysis. We proceed with the analysis of initial value formulation of general relativity to argue that causality severely limits what observable effects can be derived from superhorizon perturbations. By constructing a Riemann normal coordinate system on initial slice we show that no infrared divergence terms arise in this coordinate system. Thus any divergences found previously can be eliminated by a local rescaling of coordinates and are unobservable. We perform an explicit analysis of the variance of the deceleration parameter for the case of single-field inflation using usual coordinates and show that the infrared-divergent terms found by Barausse et al. and Kolb et al. cancel against several additional terms not considered in their analysis. Finally, we argue that introducing isocurvature perturbations does not alter our conclusion that the accelerating expansion of the universe cannot be explained by superhorizon modes.

We calculate the full one-loop electroweak (FEW) corrections to $H^{-}\to {\tilde{\chi }}_i^0{\tilde{\chi }}_1^{-}$ in the minimal supersymmetric standard model (MSSM), and compare with the leading order (LO) corrections including the loops of the (s)quarks only in the third generation and the complete leading order (CLO) corrections including the loops of the (s)quarks in all three generations. We find that the magnitudes of the FEW corrections can be larger than 10% for $\tan \beta >30$. Moreover, comparing with the FEW corrections, both of the LO and the CLO corrections are negligibly small for mode 1 ($H^{-}\to {\tilde{\chi }}_1^0{\tilde{\chi }}_1^{-}$) when $\tan \beta <5$, and for mode 2 ($H^{-}\to {\tilde{\chi }}_2^0{\tilde{\chi }}_1^{-}$) when $\tan \beta >45$, respectively, since there are not enhancements from the Yukawa couplings. We also calculate the FEW corrections in the minimal supergravity scenario, where the FEW corrections can be larger than the LO and the CLO corrections by more than 60% and 50%, respectively.

A master action for the bosonic p-brane, interpolating between the Nambu-Goto and Polyakov formalisms, is discussed. The fundamental arbitrariness of extended structures (p-brane) embedded in spacetime manifold has been exploited to build an independent metric in the brane world volume. The cosmological term for the generic case follows naturally in the scheme. The dynamics of the structure leads to a natural emergence of the A-D-M like split of this world volume. The role of the gauge symmetries vis-à-vis reparametrization symmetries is analyzed by a constrained Hamiltonian approach.

An interesting dynamical model for dark energy which does not require extremely light scalar fields such as quintessence, and at the same time explains the (near) coincidence between the neutrino and dark energy densities is the model of dark energy coupled to mass-varying neutrinos (MaVaNs). Despite the attractions of this model, we show that, generically, this model contains a catastrophic instability which occurs when neutrinos become nonrelativistic. As a result of this instability, as neutrinos become nonrelativistic, they condense into neutrino nuggets which redshift away similar to cold dark matter, and thus cease to act as dark energy. Any stable MaVaNs dark energy model is extremely contrived and is virtually indistinguishable from a cosmological constant.

We explore BPS soliton configurations in $N=2$ supersymmetric Yang-Mills theory with matter fields arising from parallel D3 branes on D7 branes. Especially we focus on a two parameter family of $1/8$ BPS equations, dyonic objects, and $1/8$ BPS objects and raise a possibility of the absence of BPS vortices when the number of D3 branes is larger than that of D7 branes.

We give the light-cone gauge calculation of the one-loop on-shell scattering amplitudes for gluon-gluon scattering which violate helicity conservation. We regulate infrared divergences by discretizing the $p^{+}$ integrations, omitting the terms with $p^{+}=0$. Collinear divergences are absent diagram by diagram for the helicity nonconserving amplitudes. We also employ a novel ultraviolet regulator that is natural for the light-cone worldsheet description of planar Feynman diagrams. We show that these regulators give the known answers for the helicity nonconserving one-loop amplitudes, which do not suffer from the usual infrared vagaries of massless particle scattering. For the maximal helicity violating process we elucidate the physics of the remarkable fact that the loop momentum integrand for the on-shell Green function associated with this process, with a suitable momentum routing of the different contributing topologies, is identically zero. We enumerate the counterterms that must be included to give Lorentz covariant results to this order, and we show that they can be described locally in the light-cone worldsheet formulation of the sum of planar diagrams.

We study the deconfinement transition of hadronic matter into quark matter in neutron star conditions in the light of color superconductivity. Deconfinement is considered to be a first order phase transition that conserves color and flavor. It gives a short-lived ($\tau \sim {\tau }_{\mathrm{weak}}$) transitory colorless-quark-phase that is not in $\beta$-equilibrium. We deduce the equations governing deconfinement when quark pairing is allowed and find the regions of the parameter space (pairing gap $\Delta$ versus bag constant $B$) where deconfinement is possible inside cold neutron stars. We show that for a wide region of ($B,\Delta$) a pairing pattern is reachable within a strong interaction timescale, and the resulting “2SC-like” phase is preferred energetically to the unpaired phase. We also show that although $\beta$-stable hybrid star configurations are known to be possible for a wide region of the ($B,\Delta$)-space, many of these configurations could not form in practice because deconfinement is forbidden, i.e. the here studied non-$\beta$-stable intermediate state cannot be reached.

The phase diagram of three-flavor quark matter under compact star constraints is investigated within a Nambu–Jona-Lasinio model. Global color and electric charge neutrality is imposed for $\beta$-equilibrated superconducting quark matter. The constituent quark masses and the diquark condensates are determined self-consistently in the plane of temperature and quark chemical potential. Both strong and intermediate diquark coupling strengths are considered. We show that in both cases, gapless superconducting phases do not occur at temperatures relevant for compact star evolution, i.e., below $T\sim 50\mathrm{MeV}$. The stability and structure of isothermal quark star configurations are evaluated. For intermediate coupling, quark stars are composed of a mixed phase of normal (NQ) and two-flavor superconducting (2SC) quark matter up to a maximum mass of $1.21M_{\odot }$. At higher central densities, a phase transition to the three-flavor color flavor locked (CFL) phase occurs and the configurations become unstable. For the strong diquark coupling we find stable stars in the 2SC phase, with masses up to $1.33M_{\odot }$. A second family of more compact configurations (twins) with a CFL quark matter core and a 2SC shell is also found to be stable. The twins have masses in the range $1.30\dots 1.33M_{\odot }$. We consider also hot isothermal configurations at temperature $T=40\mathrm{MeV}$. When the hot maximum mass configuration cools down, due to emission of photons and neutrinos, a mass defect of $0.1M_{\odot }$ occurs and two final state configurations are possible.

We derive the effective Lagrangian of the physical four-dimensional fields in the Randall-Sundrum (RS) model, and use this to calculate the Newtonian gravitational potential between two point sources on the brane. The effect of the radion is emphasized, and it is shown to disappear when the hidden brane is taken to infinity, i.e. when we only have one brane. As a preliminary, we derive the corresponding Lagrangian in the simpler geometry of a flat spacetime with one extra dimension compactified on a torus. We also study the gauge invariance of the theory, and note that the massless vector field that is present for the torus disappears in the RS model because of the orbifold symmetry.

A quantum theory of spherically symmetric thin shells of null dust and their gravitational field is studied. In Nucl. Phys. B603, 555 (2001), it has been shown how superpositions of quantum states with different geometries can lead to a solution of the singularity problem and black hole information paradox: the shells bounce and re-expand and the evolution is unitary. The corresponding scattering times will be defined in the present paper. To this aim, a spherical mirror of radius $R_m$ is introduced. The classical formula for scattering times of the shell reflected from the mirror is extended to quantum theory. The scattering times and their spreads are calculated. They have a regular limit for $R_m\to 0$ and they reveal a resonance at $E_m=c^4{R}_m/2G$. Except for the resonance, they are roughly of the order of the time the light needs to cross the flat space distance between the observer and the mirror. Some ideas are discussed of how the construction of the quantum theory could be changed so that the scattering times become considerably longer.

We consider Kerr–de Sitter spacetimes and evaluate their mass, angular momentum, and entropy according to the boundary counterterm prescription. We provide a physical interpretation for angular velocity and angular momentum at future/past infinity. We show that the entropy of the four-dimensional Kerr–de Sitter spacetimes is less than of pure de Sitter (dS) spacetime in agreement with the entropic $N$ bound. Moreover, we show that maximal mass conjecture which states “any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity” is respected by asymptotically de Sitter spacetimes with rotation. We furthermore consider the possibility of strengthening the conjecture to state that “any asymptotically dS spacetime will have mass greater than dS if and only if it has a cosmological singularity” and find that Kerr–de Sitter spacetimes do not respect this stronger statement. We investigate the behavior of the $c$ function for the Kerr–de Sitter spacetimes and show that it is no longer isotropic. However an average of the $c$ function over the angular variables yields a renormalization group flow in agreement with the expansion of spacetime at future infinity.

Using the Ehlers transformation along with the gravitoelectromagnetic approach to stationary spacetimes we start from the Morgan-Morgan disk spacetime (without radial pressure) as the seed metric and find its corresponding stationary spacetime. As expected from the Ehlers transformation the stationary spacetime obtained suffers from a NUT-type singularity and the new parameter introduced in the stationary case could be interpreted as the gravitomagnetic monopole charge (or the NUT factor). Some of the properties of this spacetime including its particle velocity distribution, gravitational redshift, stability, and energy conditions are discussed.

We study a two-level atom in interaction with a real massless scalar quantum field in a spacetime with a reflecting boundary. The presence of the boundary modifies the quantum fluctuations of the scalar field, which in turn modifies the radiative properties of atoms. We calculate the rate of change of the mean atomic energy of the atom for both inertial motion and uniform acceleration. It is found that the modifications induced by the presence of a boundary make the spontaneous radiation rate of an excited inertial atom oscillate near the boundary and this oscillatory behavior may offer a possible opportunity for experimental tests for geometrical (boundary) effects in flat spacetime. While for accelerated atoms, the transitions from ground states to excited states are found to be possible even in a vacuum due to changes in the vacuum fluctuations induced by both the presence of the boundary and the acceleration of atoms, and this can be regarded as an actual physical process underlying the Unruh effect.

The cosmological vacuum decay scenario recently proposed by Wang and Meng [Classical Quantum Gravity 22, 283 (2005)] is rediscussed. From thermodynamic arguments it is found that the $ϵ$ parameter quantifying the vacuum decay rate must be positive in the presence of particle creation. If there is no particle creation, the proper mass of Cold Dark Matter (CDM) particles is necessarily a time-dependent quantity, scaling as $m(t)=m_{o}a(t{)}^{ϵ}$. By considering the presence of baryons in the cosmological scenario, it is also shown that their dynamic effect is to alter the transition redshift $z_{*}$ (the redshift at which the Universe switches from decelerating to accelerating expansion), predicting values of $z_{*}$ compatible with current estimates based on type Ia supernova. In order to constrain the ${\Omega }_m-ϵ$ plane, a joint statistical analysis involving the current supernovae observations, gas mass fraction measurements in galaxy clusters and CMB data is performed. At $95\%$ c.l. it is found that the vacuum decay rate parameter lies on the interval $ϵ=0.06\pm 0.10$. The possibility of a vacuum decay into photons is also analyzed. In this case, the energy density of the radiation fluid scales as ${\rho }_r={\rho }_{ro}{a}^{-4+ϵ}$, and its temperature evolution law obeys $T(t)=T_{o}a(t{)}^{ϵ/4-1}$.