We study rotating strings with multiple spins in the background of ${\mathrm{AdS}}_5\times {\mathrm{T}}^{1,1},$ which is dual to an $\mathcal{N}=1\mathrm{}$ superconformal field theory with global symmetry $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}\times U\left(1\right)\mathrm{}$ via the AdS conformal field theory correspondence. We analyze the limiting behavior of macroscopic strings and discuss the identification of the dual operators and how their anomalous dimensions should behave as the global charges vary. The class of string solutions we find are dual to the operators in the $\mathrm{SU}\left(2\right)\mathrm{}$ subsector, and our result implies that the one-loop planar dilatation operator restricted to the $\mathrm{SU}\left(2\right)\mathrm{}$ subsector should be equivalent to the Hamiltonian of the integrable Heisenberg spin chain.

First, we diagonalize the bc-ghost 3-string Neumann matrices using the technique described in Phys. Rev. D 68, 066003 (2003). Their eigenvalues are in complete agreement with the previous authors. Second, we diagonalize the N-string gluing vertices for the bosonized ghost system. Third, we verify the descent and associativity relations for the combined bosonic matter+ghost gluing vertices. We find that in order for these relations to be true, the vertices must be normalized by the factor ${\mathcal{Z}}_N.$ Here ${\mathcal{Z}}_N$ is the partition function of the bosonic matter+ghost CFT on the gluing surface, which is the unit disk with the Neumann boundary conditions and the midpoint conelike singularity specified by the angle excess $\pi \left(N-2\right).$

In order to overcome the ambiguity problem in the identification of mathematical objects in noncommutative theory with physical observables, a quantum mechanical system coupled to the noncommutative (NC) U(1) gauge field in the noncommutative space is reformulated by making use of the unitarized Seiberg-Witten map, and applied to the Aharonov-Bohm (AB) and Hall effects of the NC U(1) gauge field. Retaining terms only up to linear order in the NC parameter $\theta ,$ we find that the AB topological phase and the Hall conductivity both have the same formulas as those of the ordinary commutative space with no $\theta$ dependence.

We examine the QCD perturbation series at large orders for different values of the “large ${\beta }_0$ renormalization scale.” It is found that if we let this scale grow exponentially with the order, the divergent series can be turned into an expansion that converges to the Borel integral, with a certain cutoff. In the case of the first IR renormalon at $2/{\beta }_0,$ corresponding to a dimension four operator in the operator product expansion, this qualitatively improves the perturbative predictions. Furthermore, our results allow us to establish formulations of the principle of minimal sensitivity and the fastest apparent convergence criterion that result in a convergent expansion.

It is shown that light-front thermal field theory is equivalent to conventional thermal field theory. The proof is based on the use of spectral representations, and applies to all Lagrangians for which such equivalence has been proven at zero temperature. It is also pointed out that conventional spectral functions can be used to express light-front finite temperature free propagators. As an application of our approach, we derive the light-front finite temperature spin 1/2 fermion propagator in full Dirac space.

We construct effective Lagrangians of the Veneziano-Yankielowicz (VY) type for two nonsupersymmetric theories which are orientifold daughters of supersymmetric gluodynamics (containing one Dirac fermion in the two-index antisymmetric or symmetric representation of the gauge group). Since the parent and daughter theories are planar equivalent, at $\overrightarrow{N}\infty$ the effective Lagrangians in the orientifold theories basically coincide with the bosonic part of the VY Lagrangian. We depart from the supersymmetric limit in two ways. First, we consider finite (albeit large) values of N. Then $1/N$ effects break supersymmetry. We suggest seemingly the simplest modification of the VY Lagrangian which incorporates these $1/N$ effects, leading to a nonvanishing vacuum energy density. We analyze the spectrum of the finite-$N$ nonsupersymmetric daughters. For $N=3\mathrm{}$ the two-index antisymmetric representation (one flavor) is equivalent to one-flavor QCD. We show that in this case the scalar quark-antiquark state is heavier than the corresponding pseudoscalar state, “${\eta }^{\prime }.$” Second, we add a small fermion mass term. The fermion mass term breaks supersymmetry explicitly. The vacuum degeneracy is lifted. The parity doublets split. We evaluate the splitting. Finally, we include the $\theta$ angle and study its implications.

For the meron configuration of the $\mathrm{SU}\left(2\right)\mathrm{}$ gauge field in four-dimensional Minkowskii spacetime, the decomposition into an isovector field $\mathit{n},$ isoscalar fields $\rho$ and $\sigma ,$ and a $U\left(1\right)\mathrm{}$ gauge field $C_{\mu }$ is attained by solving the consistency condition for $\mathit{n}.$ The resulting $\mathit{n}$ turn out to possess two singular points, behave like a monopole-antimonopole pair, and reduce to the conventional hedgehog in a special case. The $C_{\mu }$ field also possesses singular points, while $\rho$ and $\sigma$ are regular everywhere.

This article is based on the covariant canonical formalism and corresponding symplectic structure on phase space developed by Witten, Zuckerman, and others in the context of field theory. After recalling the basic principles of this procedure, we construct the conserved bilinear symplectic current for generic elastic string models. These models describe current carrying cosmic strings evolving in an arbitrary curved background spacetime. Particular attention is paid to the special case of the chiral string for which the worldsheet current is null. Different formulations of the chiral string action are discussed in detail, and as a result the integrability property of the chiral string is clarified.

In $\mathcal{N}=2\mathrm{}$ super Yang-Mills theory the charges of a Bogomol’nyi-Prasad-Sommerfield (BPS) state shift under the transition to a dual description of the theory. In particular, in the theory with matter duality, transformations may convert a bound state to an unbound one as predicted by Seiberg and Witten from considerations of the monodromies around the moduli space singularities. The physical mechanism of such behavior on the semiclassical level can be established explicitly through the consideration of soliton-fermion classical field configurations. The problem reduces to the investigation of the fermion spectrum in a slowly varying background monopole field. The behavior of the solutions to classical equations allows one to observe the BPS bound state “decay” in vivo.

We consider a self-consistent system of interacting spinor and scalar fields within the framework of a Bianchi type-I (BI) cosmological model filled with perfect fluid. The interacting term in the Lagrangian is chosen in the form of derivative coupling, i.e., ${\mathcal{L}}_{\mathrm{int}}=(\lambda /2){\phi }_{,\alpha }{\phi }^{,\alpha }F.\mathrm{}$ Here F is a power or trigonometric function of the invariants I and/or J constructed from bilinear spinor forms $S=\overline{\psi }\psi$ and $P=i\overline{\psi }{\gamma }^5\psi .$ Self-consistent solutions to the spinor, scalar, and BI gravitational field equations are obtained. The problems of an initial singularity and the asymptotically isotropization process of the initially anisotropic space-time are studied. The role of the cosmological constant $(\Lambda$ term) in the evolution of a BI Universe is studied. It is shown that a positive $\Lambda$ generates an oscillatory mode of expansion of the BI model, whereas if F in ${\mathcal{L}}_{\mathrm{int}}$ is chosen to be a trigonometric function of its arguments, there exists a nonexponential mode of evolution even with a negative $\Lambda .$ It is shown also that for a suitable choice of problem parameters the present model allows regular solutions without a broken dominant energy condition.

We perform an analytic late time analysis for maximal slicing of the Reissner-Nordström black hole spacetime. In particular, we discuss the collapse of the lapse in terms of its late time behavior at the throat and at the event horizon for the even and the puncture lapse. In the latter case we also determine the value of the lapse at the puncture. Furthermore, in the limit of late times slice stretching effects are studied as they arise for maximal slicing of puncture evolutions. We perform numerical experiments for a Schwarzschild black hole with puncture lapse and find agreement with the analytical results.

We consider a spacetime foam model of the Schwarzschild horizon, where the horizon consists of Planck size black holes. According to our model the entropy of the Schwarzschild black hole is proportional to the area of its event horizon. It is possible to express geometrical arguments to the effect that the constant of proportionality is, in natural units, equal to one-quarter.

Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a pole part [proportional to $\left(d-{3)}^{-1}\right]$ which diverges as the space dimension d tends to 3. It is proven that the pole part can be renormalized away by introducing suitable shifts of the two world-lines representing the point masses, and that the same shifts renormalize away the pole part of the “bulk” metric tensor $g_{\mu \nu }{(x}^{\lambda }).\mathrm{}$ The ensuing, finite renormalized equations of motion are then found to belong to the general parametric equations of motion derived by an extended Hadamard regularization method, and to uniquely determine the 3PN ambiguity parameter $\lambda$ to be $\lambda =-1987/3080.$ This value is fully consistent with the recent determination of the equivalent 3PN “static ambiguity” parameter, ${\omega }_s=0,$ by a dimensional-regularization derivation of the Hamiltonian in Arnowitt-Deser-Misner coordinates. Our work provides a new, powerful check of the consistency of the dimensional regularization method within the context of the classical gravitational interaction of point particles.

Within the scope of the Bianchi type VI models, the self-consistent system of nonlinear spinor field and gravitational fields is considered. Exact self-consistent solutions to the spinor and gravitational field equations are obtained for a special choice of spatial inhomogeneity and nonlinear spinor term. The role of inhomogeneity in the evolution of spinor and gravitational field is studied. Some solutions allow an oscillating behavior of the Universe’s volume. It should be emphasized that for a suitable choice of spinor field nonlinearity some of these solutions are nonsingular at all space-time points.

We study the boundary value problem for stationary rotating black hole solutions to the five-dimensional vacuum Einstein equation. Assuming the existence of two additional commuting rotational Killing vector fields and sphericity of the horizon topology, we show that a black hole with a regular event horizon is uniquely characterized by its mass and a pair of angular momenta.

We perform a series of two-dimensional, axisymmetric, magnetohydrodynamic simulations of the rotational collapse of a supernova core. In order to calculate the waveforms of the gravitational wave, we derive the quadrupole formula including the contributions from the electromagnetic fields. Recent stellar evolution calculations imply that the magnetic fields of the toroidal components are much stronger than those of the poloidal ones at the presupernova stage. Thus we systematically investigate the effects of the toroidal magnetic fields on the amplitudes and waveforms of the gravitational wave. Furthermore, we employ two kinds of the realistic equation of states which are often used in supernova simulations. Then, we investigate the effects of the equation of states on the gravitational wave signals. As for microphysics, we take into account the electron capture and neutrino transport by the so-called leakage scheme. With these computations, we find that the peak amplitudes of the gravitational wave are lowered by an order of 10% for models with the strongest toroidal magnetic fields. However, the peak amplitudes are mostly within the sensitivity range of laser interferometers such as TAMA and the first LIGO for a source at a distance of 10 kpc. Furthermore, we point out that the amplitudes of second peaks are still within the detection limit of the first LIGO for the source, although the characteristics of second peaks are reduced by the magnetic fields. We stress the importance of the detection, since it will give us information about the angular momentum distribution of massive evolved stars. When we compare the gravitational waves from the two realistic equations of state, significant differences are not found, except that the typical frequencies of the gravitational wave become slightly higher for the softer equation of state.

We give an explicit formulation of the time dependent AdS/CFT correspondence when there are multiple vacua present in the Lorentzian signature. By computing sample two point functions we show how different amplitudes are related by cosmological particle production. We illustrate our methods in two example spacetimes: (a) a “bubble of nothing” in AdS space, and (b) an asymptotically locally AdS spacetime with a bubble of nothing on the boundary. In both cases the $\alpha$ vacua of de Sitter space make an interesting appearance.

A detailed study is presented of the counterrotating model (CRM) for generic electrovacuum static axially symmetric relativistic thin disks without radial pressure. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We also find explicit expressions for the energy densities, charge densities and velocities of the counterrotating fluids. We then show that this constraint can be satisfied if we take the two counterrotating streams as circulating along electrogeodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electrogeodesics nor take the two counterrotating tangential velocities as equal and opposite. Four simple families of models of counterrotating charged disks based on Chazy-Curzon-type, Zipoy-Voorhees-type, Bonnor-Sackfield-type, and Kerr-type electrovacuum solutions are considered where we obtain some disks with a CRM well behaved. The models are constructed using the well-known “displace, cut and reflect” method extended to solutions of vacuum Einstein-Maxwell equations.

It is usually supposed that inflation is of the slow-roll variety and that the inflaton generates the primordial curvature perturbation. According to the curvaton hypothesis, inflation need not be slow-roll, and if it is, the inflaton generates a negligible curvature perturbation. We find that the construction of slow-roll inflation models becomes much easier under this hypothesis. Also, thermal inflation followed by fast-roll becomes viable, with no slow-roll inflation at all.

We study the renormalized energy-momentum tensor (EMT) of cosmological scalar fluctuations during the slow-rollover regime for chaotic inflation with a quadratic potential and find that it is characterized by a negative energy density which grows during slow rollover. We also approach the back-reaction problem as a second-order calculation in perturbation theory, finding no evidence that the back reaction of cosmological fluctuations is a gauge artifact. In agreement with the results for the EMT, the average expansion rate is decreased by the back reaction of cosmological fluctuations.