Flat Spacetime Background Research Articles

Dark energy and dark matter from nonlocal ghost-free gravity theory

We suggest a class of generally covariant ghost-free nonlocal gravity models generating de Sitter or anti-de Sitter background with an arbitrary value of the effective cosmological constant and featuring a mechanism of dark matter simulation. These models interpolate between the general relativistic phase on a flat spacetime background and their strongly coupled infrared (anti-)de Sitter phase with two propagating massless graviton modes.

Born–Infeld axion–dilaton electrodynamics and electromagnetic confinement

A generalization of Born–Infeld non-linear vacuum electrodynamics involving axion and dilaton fields is constructed with couplings dictated by electromagnetic duality and SL(2,R) symmetries in the weak field limit. Besides the Newtonian gravitational constant the model contains a single fundamental coupling parameter b0. In the absence of axion and dilaton interactions it reduces in the limit b0↦∞ to Maxwellʼs linear vacuum theory while for finite b0 it reduces to the original Born–Infeld model. The spherically symmetric static sector of the theory is explored in a flat background spacetime in the Jordan frame where numerical evidence suggests the existence of axion–dilaton bound states possessing confined electric flux.

Holographic insights and puzzles

AbstractThe talk is composed of two parts, both set within the AdS/CFT context. In the first part, I discuss holographic insight into strongly coupled field theory in a black hole background. I conjecture two new gravitational solutions, dubbed black funnels and black droplets, which describe two distinct deconfined phases in the field theory at finite temperature. I also briefly mention puzzles associated with an analogous set‐up in a rotating black hole background. In the second part of the talk, I discuss time‐dependent states in a CFT on flat spacetime background, exemplified by the conformal soliton flow. Here I focus on puzzles regarding the nature of entropy in time‐evolving states and its holographic dual.

Dynamical Symmetry Breaking in RN Quantum Gravity

We show that in the RN gravitation model, there is no dynamical symmetry breaking effect in the formalism of the Schwinger-Dyson equation (in flat background space-time). A general formula for the second variation of the gravitational action is obtained from the quantum corrections hμν (in arbitrary background metrics).

Angularly excited and interacting boson stars andQballs

We study angularly excited as well as interacting nontopological solitons, the so-called $Q$ balls, and their gravitating counterparts, the so-called boson stars, in $3+1$ dimensions. $Q$ balls and boson stars carry a nonvanishing Noether charge and arise as solutions of complex scalar field models in a flat space-time background and coupled minimally to gravity, respectively. We present examples of interacting $Q$ balls that arise due to angular excitations, which are closely related to the spherical harmonics. We also construct explicit examples of rotating boson stars that interact with nonrotating boson stars. We observe that rotating boson stars tend to absorb the nonrotating ones for increasing, but reasonably small gravitational coupling. This is a new phenomenon as compared to the flat space-time limit and is related to the negative contribution of the rotation term to the energy density of the solutions. In addition, our results indicate that a system of a rotating and nonrotating boson star can become unstable if the direct interaction term in the potential is large enough. This instability is related to the appearance of ergoregions.

THE SUPERSTRING WORLD SHEET IN CURVED SPACE–TIME

The heterotic superstring theory is formulated on the world sheet hab(τ,σ), in a flat space–time background [Formula: see text], by combining a 26-dimensional left-moving sector, consisting only of bosonic fields [Formula: see text], with a 10-dimensional right-moving sector, consisting of bosonic fields [Formula: see text] and Majorana–Weyl fermionic fields ψA(τ - σ), the string coordinates in 10-dimensional space–time being the sum [Formula: see text] and the right-moving sector supersymmetric due to the decoupling of left- and right-moving modes for closed strings. Here, we generalize the background to a curved space–time ĝAB(XC). The equation of motion for XA(τ,σ), given by Short, is then a non-linear modification of the linear wave equation □XA = 0 which yields decoupled left- and right-moving sectors in flat space–time. The linearity of the transverse modes can be maintained, however, if the metric, after reduction to four dimensions, is allowed to depend only upon co-moving time t ∝ X0, although it can be anisotropic, gij = gij(X0). Specializing to the isotropic, Friedmann cosmological space–time ds2 = dt2 - r2(t) dx2, where the radius function of the three-space dx2, assumed flat, is r(t), with d ln r/dt = 2/3γt for a perfect-fluid source whose pressure and energy-density are related by p = (γ - 1)ρ, we find that the string coordinates Xα(τ,σ)(α = 1,2,3), multiplied by the overall prefactor r ≡ t2/3γ, are purely oscillatory only in Minkowski space or for the value γ = 2/3. This result is equivalent to requiring that the Nordström energy-density ρ N ≡ (3γ - 2)ρ vanish. The case ρ = 2/3 corresponds to a space–time generated by an ensemble of cosmic strings, including the superstrings themselves in a self-consistent solution containing no other matter, and defines the Milne universe. The string is only world-sheet-supersymmetric if ρ N = 0, that is if ρ = 0 or γ = 2/3.

MASS-GAPS AND SPIN CHAINS FOR (SUPER)MEMBRANES

We present a method for computing the nonperturbative mass-gap in the theory of bosonic membranes in flat background space–times. The analysis is extended to the study of membranes coupled to background fluxes as well. The computation of mass-gaps is carried out using a matrix regularization of the membrane Hamiltonians. The mass gap is shown to be naturally organized as an expansion in a "hidden" parameter, which turns out to be [Formula: see text] being the related to the dimensionality of the background space. We then proceed to develop a large N perturbation theory for the membrane/matrix-model Hamiltonians around the quantum/mass corrected effective potential. The same parameter that controls the perturbation theory for the mass gap is also shown to control the Hamiltonian perturbation theory around the effective potential. The large N perturbation theory is then translated into the language of quantum spin chains and the one-loop spectra of various bosonic matrix models are computed by applying the Bethe ansatz to the one-loop effective Hamiltonians for membranes in flat space–times. The spin chains corresponding to the large N effective Hamiltonians for the relevant matrix models are generically not integrable. However, we are able to find large integrable subsectors for all the spin chains of interest. Moreover, the continuum limits of the spin chains are mapped to integrable Landau–Lifschitz models even if the underlying spin chains are not integrable. Apart from membranes in flat space–times, the recently proposed matrix models (arXiv:hep-th/0607005) for noncritical membranes in plane wave type space–times are also analyzed within the paradigm of quantum spin chains. The bosonic sectors of all the models proposed in arXiv:hep-th/0607005 are diagonalized at the one-loop level and an intriguing connection between the existence of supersymmetric vacua and one-loop integrability is also presented.

A VACUUM-LIKE CONFIGURATION IN GENERAL RELATIVITY AS A MANIFESTATION OF A LORENTZ-INVARIANT MODE OF FIVE-DIMENSIONAL GRAVITY

A Lorentz-invariant cosmological model is constructed within the framework of five-dimensional gravity. The five-dimensional theorem which is analogical to the generalized Birkhoff theorem is proved, that corresponds to the Kaluza's "cylinder condition." The five-dimensional vacuum Einstein equations have an integral of motion corresponding to this symmetry, the integral of motion is similar to the mass function in general relativity (GR). Space closure with respect to the extra dimensionality follows from the requirement of the absence of a conical singularity. Thus, the Kaluza–Klein (KK) model is realized dynamically as a Lorentz-invariant mode of five-dimensional general relativity. After the dimensional reduction and conformal mapping the model is reduced to the GR configuration. It contains a scalar field with a vanishing conformally invariant energy–momentum tensor on the flat space–time background. This zero mode can be interpreted as a vacuum configuration in GR. As a result the vacuum-like configuration in GR can be considered as a manifestation of the Lorentz-invariant empty five-dimensional space.

The Casimir effect of Reissner–Nordström black hole

The stress tensor of a massless scalar field satisfying a mixed boundary condition in a (1+1)-dimensional Reissner–Nordstrom black hole background is calculated by using Wald's axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.

Towards absorbing outer boundaries in general relativity

We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations on a subset of flat spacetime of the form [0, T] × BR, where BR is a ball of radius R, and analyse different kinds of boundary conditions on ∂BR. Our main results are as follows. (i) We give an explicit analytic example showing that boundary conditions obtained from freezing the incoming characteristic fields to their initial values are not compatible with the constraints. (ii) With the help of the exact solutions constructed, we determine the amount of artificial reflection of gravitational radiation from constraint-preserving boundary conditions which freeze the Weyl scalar Ψ0 to its initial value. For monochromatic radiation with wave number k and arbitrary angular momentum number ℓ ⩾ 2, the amount of reflection decays as (kR)−4 for large kR. (iii) For each L ⩾ 2, we construct new local constraint-preserving boundary conditions which perfectly absorb linearized radiation with ℓ ⩽ L. (iv) We generalize our analysis to a weakly curved background of mass M and compute first-order corrections in M/R to the reflection coefficients for quadrupolar odd-parity radiation. For our new boundary condition with L = 2, the reflection coefficient is smaller than that for the freezing Ψ0 boundary condition by a factor of M/R for kR > 1.04. Implications of these results for numerical simulations of binary black holes on finite domains are discussed.

TACHYON MONOPOLE

The property and gravitational field of global monopole of tachyon are investigated in a four-dimensional static space–time. We give an exact solution of the tachyon field in the flat space–time background. Using the linearized approximation of gravity, we get the approximate solution of the metric. We also solve analytically the coupled Einstein and tachyon field equations which is beyond the linearized approximation to determine the gravitational properties of the monopole solution. We find that the metric of tachyon monopole represents an asymptotically AdS space–time with a small effective mass at the origin. We show that this relatively tiny mass is actually negative, as it is in the case of ordinary scalar field.

D-brane boundary states in the pure spinor superstring

We study the construction of D-brane boundary states in the pure spinor formalism for the quantisation of the superstring. This is achieved both via a direct analysis of the definition of D-brane boundary states in the pure spinor conformal field theory, as well as via comparison between standard RNS and pure spinor descriptions of the superstring. Regarding the map between RNS and pure spinor formulations of the superstring, we shed new light on the tree level zero mode saturation rule. Within the pure spinor formalism we propose an explicit expression for the D-brane boundary state in a flat spacetime background. While the non-zero mode sector mostly follows from a simple understanding of the pure spinor conformal field theory, the zero mode sector requires a deeper analysis which is one of the main points in this work. With the construction of the boundary states at hand, we give a prescription for calculating scattering amplitudes in the presence of a D-brane. Finally, we also briefly discuss the coupling to the world-volume gauge field and show that the D-brane low-energy effective action is correctly reproduced.

New axially symmetric Yang-Mills-Higgs solutions with negative cosmological constant

We construct numerically new axially symmetric solutions of SU(2) Yang-Mills-Higgs theory in $(3+1)$ anti-de Sitter spacetime. Two types of finite energy, regular configurations are considered: multimonopole solutions with magnetic charge $n>1$ and monopole-antimonopole pairs with zero net magnetic charge. A somewhat detailed analysis of the boundary conditions for axially symmetric solutions is presented. The properties of these solutions are investigated, with a view to compare with those on a flat spacetime background. The basic properties of the gravitating generalizations of these configurations are also discussed.

Publisher's Note: M theory model of a big crunch/big bang transition [Phys. Rev. D70, 106004 (2004)

We consider a picture in which the transition from a big crunch to a big bang corresponds to the collision of two empty orbifold planes approaching each other at a constant non-relativistic speed in a locally flat background space-time, a situation relevant to recently proposed cosmological models. We show that $p$-brane states which wind around the extra dimension propagate smoothly and unambiguously across the orbifold plane collision. In particular we calculate the quantum mechanical production of winding M2-branes extending from one orbifold to the other. We find that the resulting density is finite and that the resulting gravitational back-reaction is small. These winding states, which include the string theory graviton, can be propagated smoothly across the transition using a perturbative expansion in the membrane tension, an expansion which from the point of view of string theory is an expansion in {\it inverse} powers of $\alpha'$. We argue that interactions should be well-behaved because the string coupling tends to zero at the crunch. The production of massive Kaluza-Klein states should also be exponentially suppressed for small collision speeds. We contrast this good behavior with that found in previous studies of strings in Lorentzian orbifolds.

M theory model of a big crunch/big bang transition

We consider a picture in which the transition from a big crunch to a big bang corresponds to the collision of two empty orbifold planes approaching each other at a constant nonrelativistic speed in a locally flat background space-time, a situation relevant to recently proposed cosmological models. We show that $p$-brane states which wind around the extra dimension propagate smoothly and unambiguously across the orbifold plane collision. In particular we calculate the quantum mechanical production of winding M2-branes extending from one orbifold to the other. We find that the resulting density is finite and that the resulting gravitational backreaction is small. These winding states, which include the string theory graviton, can be propagated smoothly across the transition using a perturbative expansion in the membrane tension, an expansion which from the point of view of string theory is an expansion in inverse powers of ${\ensuremath{\alpha}}^{\ensuremath{'}}$. The conventional description of a crunch based on Einstein general relativity, involving Kasner or mixmaster behavior is misleading, we argue, because general relativity is only the leading order approximation to string theory in an expansion in positive powers of ${\ensuremath{\alpha}}^{\ensuremath{'}}$. In contrast, in the M theory setup we argue that interactions should be well behaved because of the smooth evolution of the fields combined with the fact that the string coupling tends to zero at the crunch. The production of massive Kaluza-Klein states should also be exponentially suppressed for small collision speeds. We contrast this good behavior with that found in previous studies of strings in Lorentzian orbifolds.

GAUGINO CONDENSATION IN HETEROTIC FIVE-BRANE BACKGROUND

The gaugino propagator is calculated by explicitly considering the propagation of a heterotic string between two different points in spacetime using the nontrivial worldsheet conformal field theory for the five-brane background. We find that there are no propagations of gaugino which is in the spinor representation of the nontrivial four-dimensional space of the five-brane background. This result is consistent with the arguments on the fermion zero-modes of the five-brane background in the low-energy heterotic supergravity theory. Furthermore, assuming the continuous limit to the flat spacetime background at the place far away from the five-brane, we suggest an effective propagator which is effective only at the place far away from the five-brane in the flat spacetime limit. From the effective propagator we evaluate a possible gaugino pair condensation. The result is consistent with the suggested scenario of the gaugino condensation in the five-brane background in the low-energy heterotic supergravity theory.

Comparison of the Oscillatory Behavior of a Gravitating Nambu-Goto String and a Test String

Comparison of the oscillatory behavior of a gravitating infinite Nambu-Goto string and a test string is investigated using the general relativistic gauge invariant perturbation technique with two infinitesimal parameters on a flat spacetime background. Due to the existence of the pp-wave exact solution, we see that the conclusion that the dynamical degree of freedom of an infinite Nambu-Goto string is completely determined by that of gravitational waves, which was reached in our previous works [K. Nakamura, A. Ishibashi and H. Ishihara, Phys. Rev. D{\bf 62} (2002), 101502(R); K. Nakamura and H. Ishihara, Phys. Rev. D{\bf 63} (2001), 127501.], do not contradict to the dynamics of a test string. We also briefly discuss the implication of this result.

MAGNETIC CHARGE, ANGULAR MOMENTUM AND NEGATIVE COSMOLOGICAL CONSTANT

We argue that there are no axially symmetric rotating monopole solutions for a Yang–Mills–Higgs theory in flat space–time background. We construct axially symmetric Yang–Mills–Higgs solutions in the presence of a negative cosmological constant, carrying magnetic charge n and a nonvanishing electric charge. However, these solution are also nonrotating.

Advantages of a modified ADM formulation: Constraint propagation analysis of the Baumgarte-Shapiro-Shibata-Nakamura system

Several numerical relativity groups are using a modified Arnowitt-Deser-Misner (ADM) formulation for their simulations, which was developed by Nakamura and co-workers (and widely cited as the Baumgarte-Shapiro-Shibata-Nakamura system). This so-called BSSN formulation is shown to be more stable than the standard ADM formulation in many cases, and there have been many attempts to explain why this reformulation has such an advantage. We try to explain the background mechanism of the BSSN equations by using an eigenvalue analysis of constraint propagation equations. This analysis has been applied and has succeeded in explaining other systems in our series of works. We derive the full set of the constraint propagation equations, and study it in the flat background space-time. We carefully examine how the replacements and adjustments in the equations change the propagation structure of the constraints, i.e., whether violation of constraints (if it exists) will decay or propagate away. We conclude that the better stability of the BSSN system is obtained by their adjustments in the equations, and that the combination of the adjustments is in a good balance, i.e., a lack of their adjustments might fail to obtain the present stability. We further propose other adjustments to the equations, which may offer more stable features than the current BSSN equations.

Correspondence principle in a PP-wave background

We discuss the correspondence point between a string state and a black hole, in a pp-wave background, and find that the answer is considerably different from that in a flat spacetime background.