Boundary conditions play an important role in the ADHMN construction of BPS monopole solutions. In this paper we show how different types of boundary conditions can be related to each other by removing monopoles to spatial infinity. In particular, we use this method to show how the jumping data naturally emerge. The results can be interpreted in the D-brane picture and provide a better understanding of the derivation of the ADHMN construction from D-branes. We comment briefly on the cases with non-Abelian unbroken symmetry and massless monopoles.

The complete set of two-loop renormalization group equations in general gauge field theories is presented. This includes the $\beta$ functions of parameters with and without a mass dimension.

We investigate the chiral anomaly for fermions in the fundamental representation on a noncommutative (fuzzy) 2-sphere. In spite of the fact that this system is realized by finite dimensional matrices and no regularization is necessary for either UV or IR, we can reproduce the correct chiral anomaly which is consistent with the calculations done in flat noncommutative space. As in the flat case, there are ambiguities in defining the chiral currents. We define the chiral currents in a gauge-invariant way and a gauge-covariant way, and show that the corresponding anomalous chiral Ward-Takahashi identities take different forms. The Ward-Takahashi identity for the gauge-invariant current contains explicit nonlocality while that for the covariant one is given by a local expression.

An exact representation of the Euclidean fermion determinant in two dimensions for centrally symmetric, finite-ranged Abelian background fields is derived. Input data are the wave function inside the field’s range and the scattering phase shift with their momenta rotated to the positive imaginary axis and fixed at the fermion mass for each partial wave. The determinant’s asymptotic limit for strong coupling and small fermion mass for square-integrable, unidirectional magnetic fields is shown to depend only on the chiral anomaly. The concept of duality is extended from one- to two-variable fields, thereby relating the two-dimensional Euclidean determinant for a class of background magnetic fields to the pair production probability in four dimensions for a related class of electric pulses. Additionally, the “diamagnetic” bound on the two-dimensional Euclidean determinant is related to the negative sign of $\partial \mathrm{Im}{S}_{\mathrm{eff}}/\partial m^2$ in four dimensions in the strong coupling, small mass limit, where $S_{\mathrm{eff}}$ is the one-loop effective action.

We analyze large gauge invariance in the non-Abelian, finite temperature context and its physical consequences for $D=3\mathrm{}$ effective actions. After briefly reviewing the structure of bundles and large gauge transformations that arise in nonsimply connected 3-manifolds and gauge groups, we discuss their connections to Chern-Simons terms and Wilson-Polyakov loops. We then provide an invariant characterization of the “Abelian” fluxes encountered in explicit computations of finite temperature effective actions. In particular we relate, and provide explicit realizations of, these fluxes to a topological index that measures the obstruction to global diagonalization of the loops around compactified time. We also explore the fate of, and exhibit some everywhere smooth, large transformations for nonvanishing index in various topologies.

Four different phases of the two-flavor quark system, i.e., the normal quark matter and color superconducting phases with and without the charge neutrality condition, are investigated in the framework of the SU(2) Nambu–Jona-Lasinio model. It is found that the color superconducting phase without charge neutrality has the lowest thermodynamic potential, and the charge neutral systems have higher thermodynamic potentials. However, the BCS pairing always lowers the system’s thermodynamic potential, i.e., for both the charged and charge neutral systems, the superconducting phases always have lower thermodynamic potentials. Compared with the BCS gap ${\Delta }_0$ for the color superconducting phase without charge neutrality, the BCS gap $\Delta$ in the charge neutral color superconducting phase has been largely reduced. When the thermodynamic potential for the charge neutral color superconducting phase equals that in the neutral normal quark matter, the diquark condensate disappears.

We study scalar, electromagnetic and gravitational perturbations of a Reissner–Nordström–anti-de Sitter (RN-AdS) spacetime, and compute its quasinormal modes (QNM’s). We confirm and extend results previously found for Schwarzschild–anti-de Sitter (S-AdS) black holes. For “large” black holes, whose horizon is much larger than the AdS radius, different classes of perturbations are almost exactly isospectral; this isospectrality is broken when the black hole’s horizon radius is comparable to the AdS radius. We provide very accurate fitting formulas for the QNM’s, which are valid for large black holes having charge $Q<\mathrm{}{Q}_{\mathrm{ext}}/3\mathrm{}$ ${(Q}_{\mathrm{ext}}$ being the extremal value of the charge). Electromagnetic and axial perturbations of large black holes are characterized by the existence of pure-imaginary (purely damped) modes. The damping of these modes tends to infinity as the black hole charge approaches the extremal value; if the corresponding mode amplitude does not tend to zero in the same limit, this implies that extremally charged RN-AdS black holes are marginally unstable. This result is relevant in view of the AdS–conformal field theory conjecture, since, according to it, the AdS QNM’s give the time scales for the approach to equilibrium in the corresponding conformal field theory.

A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer can see the minimal length further Lorentz contracted. We show that this is not the case within loop quantum gravity. In loop quantum gravity the minimal length (more precisely, minimal area) does not appear as a fixed property of geometry, but rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area. We discuss several difficulties associated with boosts and area measurement in quantum gravity. We compute the transformation of the area operator under a local boost, propose an explicit expression for the generator of local boosts, and give the conditions under which its action is unitary.

We perform a one-loop calculation of the vacuum energy of a tachyon field in anti–de Sitter space with boundary conditions corresponding to the presence of a double-trace operator in the dual field theory. Such an operator can lead to a renormalization group flow between two different conformal field theories related to each other by a Legendre transformation in the large N limit. The calculation of the one-loop vacuum energy enables us to verify the holographic c theorem one step beyond the classical supergravity approximation.

We present a new class of charged rotating solutions in the Einstein-Gauss-Bonnet gravity with a negative cosmological constant. These solutions may be interpreted as black brane solutions with two inner and outer event horizons or an extreme black brane depending on the value of the mass parameter m. We also find that the Killing vectors are the null generators of the event horizon. The physical properties of the brane such as the temperature, the angular velocity, the entropy, the electric charge and potential are computed. We also compute the action and the Gibbs potential as a function of temperature and angular velocity for the uncharged solutions, and compute the angular momentum and the mass of the black brane through the use of the Gibbs potential. We show that these thermodynamic quantities satisfy the first law of thermodynamics. We also perform a local stability analysis of the asymptotically anti–de Sitter (AdS) uncharged rotating black brane in various dimensions and show that they are locally stable for the whole phase space both in the canonical and grand-canonical ensemble. We find that the thermodynamic properties of Gauss-Bonnet rotating black branes are completely the same as those without the Gauss-Bonnet term, although the two solutions are quite different.

We investigate the inflation of the Universe in a model of four-dimensional dilatonic gravity with a massive dilaton field $\Phi .$ The dilaton simultaneously plays the role of an inflation field and a quintessence field. It yields a sequential hyperinflation with a graceful exit to asymptotic de Sitter space-time, which is an attractor, and is approached as $\exp (-\sqrt{3{\Lambda }^{\mathrm{obs}}}ct/2).\mathrm{}$ The time duration of the inflation is reciprocal to the mass of the dilaton: $\Delta t_{\mathrm{infl}}\sim m_{{}_{\Phi }}^{-1}.$ The typical number of e-folds in the simplest model of this type is shown to be realistic without fine-tuning.

This paper generalizes the static and spherically symmetric traversable wormhole geometry to a rotating axially symmetric one with a time-dependent angular velocity by means of an exact solution. It was found that the violation of the weak energy condition, although unavoidable, is considerably less severe than in the static spherically symmetric case. The radial tidal constraint is more easily met due to the rotation. Similar improvements are seen in one of the lateral tidal constraints. The magnitude of the angular velocity may have little effect on the weak energy condition violation for an axially symmetric wormhole. For a spherically symmetric one, however, the violation becomes less severe with increasing angular velocity. The time rate of change of the angular velocity, on the other hand, was found to have no effect at all. Finally, the angular velocity must depend only on the radial coordinate, confirming an earlier result.

Via a straightforward integration of the Einstein equations with a cosmological constant, all static circularly symmetric perfect fluid $2+1$ solutions are derived. The structural functions of the metric depend on the energy density, which remains, in general, arbitrary. Spacetimes for fluids satisfying linear and polytropic state equations are explicitly derived; they describe, among others, stiff matter, monatomic and diatomic ideal gases, nonrelativistic degenerate fermions, incoherent and pure radiation. As a by-product, we demonstrate the uniqueness of the constant energy density perfect fluid within the studied class of metrics. A full similarity of the perfect fluid solutions with a constant energy density of the $2+1$ and $3+1$ gravities is established.

We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For the special class of axially symmetric spacetimes with the spherical impulse generated by a snapping cosmic string we give a detailed physical interpretation of the motion of test particles.

Within the framework of geodetic brane gravity, the universe is described as a four-dimensional extended object evolving geodetically in a higher-dimensional flat background. In this paper, by introducing a new pair of canonical fields $\{\lambda {,P}_{\lambda }\},$ we derive the quadratic Hamiltonian for such a brane universe; the inclusion of matter then resembles minimal coupling. Second class constraints enter the game, invoking the Dirac brackets formalism. The algebra of the first class constraints is calculated, and the Becchi-Rouet-Stora transformation (BRST) generator of the brane universe turns out to be rank $1.$ At the quantum level, the road is open for canonical and/or functional integral quantization. The main advantages of geodetic brane gravity are (i) it introduces an intrinsic, geometrically originated, “dark matter” component, (ii) it offers, owing to the Lorentzian bulk time coordinate, a novel solution to the “problem of time,” and (iii) it enables calculation of meaningful probabilities within quantum cosmology without any auxiliary scalar field. Intriguingly, the general relativity limit is associated with $\lambda$ being a vanishing (degenerate) eigenvalue.

The emergence of time in the matter-gravity system is addressed within the context of the inflationary paradigm. A quantum minisuperspace-homogeneous minimally coupled inflaton system is studied with suitable initial conditions leading to inflation and the system is approximately solved in the limit for a large scale factor. Subsequently normal matter (either nonhomogeneous inflaton modes or lighter matter) is introduced as a perturbation and it is seen that its presence requires the coarse averaging of a gravitational wave function (which oscillates at trans-Planckian frequencies) having suitable initial conditions. Such a wave function, which is common for all types of normal matter, is associated with a “time density” in the sense that its modulus is related to the amount of time spent in a given interval (or the rate of flow of time). One is then finally led to an effective evolution equation (Schrödinger Schwinger-Tomonaga) for “normal” matter. An analogy with the emergence of a temperature in statistical mechanics is also pointed out.

We present a gauge-invariant formalism to study the evolution of curvature perturbations in a Friedmann-Robertson-Walker universe filled by multiple interacting fluids. We resolve arbitrary perturbations into adiabatic and entropy components and derive their coupled evolution equations. We demonstrate that perturbations obeying a generalized adiabatic condition remain adiabatic in the large-scale limit, even when one includes energy transfer between fluids. As a specific application we study the recently proposed curvaton model, in which the curvaton decays into radiation. We use the coupled evolution equations to show how an initial isocurvature perturbation in the curvaton gives rise to an adiabatic curvature perturbation after the curvaton decays.

We discuss the bulk Casimir effect (effective potential) for a conformal or massive scalar when the bulk represents five-dimensional anti–de Sitter (AdS) or de Sitter (dS) space with one or two four-dimensional dS branes, which may correspond to our Universe. Using zeta regularization, the interesting conclusion is reached that for both bulks in the one-brane limit the effective potential corresponding to the massive or to the conformal scalar is zero. The radion potential in the presence of quantum corrections is found. It is demonstrated that both the dS and the AdS braneworlds may be stabilized by using the Casimir force only. A brief study indicates that bulk quantum effects are relevant for brane cosmology, because they do deform the de Sitter brane. They may also provide a natural mechanism yielding a decrease of the four-dimensional cosmological constant on the physical brane of the two-brane configuration.

The Euclidean action and entropy are computed in string-generated gravity models with quadratic curvatures, and used to argue that a negative mass extremal metric is the background for hyperbolic $(k=-1)$ black hole spacetimes, k being the curvature constant of the event horizon. The entropy associated with a black hole is always positive for $k=\{0,1\}$ family. The positivity of energy condition also ensures that the $k=-1$ (extremal) entropy is non-negative.

We critically reexamine the formalism for treating the leading-twist contributions from the two-gluon Fock components occurring in hard processes that involve $\eta$ and ${\eta }^{\prime }$ mesons and establish a consistent set of conventions for the definition of the gluon distribution amplitude, the anomalous dimensions, as well as the projector of a two-gluon state onto an $\eta$ or ${\eta }^{\prime }$ state. We calculate the $\eta ,$ ${\eta }^{\prime }$-photon transition form factor to order ${\alpha }_s$ and show the cancellation of the collinear and UV singularities explicitly. An estimate of the lowest Gegenbauer coefficients of the gluon and quark distribution amplitudes is obtained from a fit to the $\eta ,$ ${\eta }^{\prime }$-photon transition form factor data. In order to elucidate the role of the two-gluon Fock component further, we analyze electroproduction of $\eta ,{\eta }^{\prime }$ mesons and the $g^{*}{g}^{*}\eta \left({\eta }^{\prime }\right)$ vertex.