Moving branes in the presence of background tachyon fields

We compute the boundary state associated with a moving Dp-brane in the presence of the open string tachyon field as a background field. The effect of the tachyon condensation on the boundary state is discussed. It leads to a boundary state associated with a lower-dimensional moving D-brane or a stationary instantonic D-brane. The former originates from condensation along the spatial directions and the latter comes from the temporal direction of the D-brane worldvolume. Using the boundary state, we also study the interaction amplitude between two arbitrary Dp ₁- and Dp ₂-branes. The long-range behavior of the amplitude is investigated, demonstrating an obvious deviation from the conventional form, due to the presence of the background tachyon field.     

Interaction of moving branes with background massless and tachyon fields in superstring theory

Using the boundary state formalism, we study a moving Dp-brane in a partially compact space-time in the presence of background fields: the Kalb-Ramond field B _μν, a U(1) gauge field A _α, and the tachyon field. The boundary state enables us to obtain the interaction amplitude of two branes with the above back-ground fields. The branes are parallel or perpendicular to each other. Because of the presence of background fields, compactification of some space-time directions, motion of the branes, and the arbitrariness of the dimensions of the branes, the system is rather general. Due to the tachyon fields and velocities of the branes, the behavior of the interaction amplitude reveals obvious differences from the conventional behavior.     

Two Moving-Angled 1-Branes with Electric Fields in a Partially Compact Spacetime

In this article, we consider two m1-branes at angle in the presence of the background electric fields, in a partially compact spacetime. The branes have motions along a common direction that is perpendicular to both of them. Using the boundary state formalism, we calculate their interaction amplitude. Some special cases of this interaction will be studied in detail.     

Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions

We consider the finite temperature Casimir effect of a massive fermionic field confined between two parallel plates, with MIT bag boundary conditions on the plates. The background spacetime is Mp+1×Tq which has q dimensions compactified to a torus. On the compact dimensions, the field is assumed to satisfy periodicity boundary conditions with arbitrary phases. Both the high temperature and the low temperature expansions of the Casimir free energy and the force are derived explicitly. It is found that the Casimir force acting on the plates is always attractive at any temperature regardless of the boundary conditions assumed on the compact torus. The asymptotic limits of the Casimir force in the small plate separation limit are also obtained.     

Transversity of a massless relativistic membrane

We consider the relativistic theory of the open two-dimensional surface which is characterized by an action proportional to the volume swept out by the surface in spacetime. It is shown that classically there are only D−3 dynamically independent transverse components among the D functions X^∓ (σ₁, σ₂, τ) which represent the world volume (D is the dimension of spacetime) and that the surface boundary moves with the velocity of light.     

Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

A slice theorem for the space of solutions of Einstein's equations

A slice for the action of a group G on a manifold X at a point x ? X is, roughly speaking, a submanifold S_x which is transverse to the orbits of G near x. Ebin and Palais proved the existence of a slice for the diffeomorphism group of a compact manifold acting on the space of all Riemannian metrics. We prove a slice theorem for the group $\text{D}$ of diffeomorphisms of spacetime acting on the space $\text{E}$ of spatially compact, globally hyperbolic solutions of Einstein's equations. New difficulties beyond those encountered by Ebin and Palais arise because of the Lorentz signature of the spacetime metrics in $\text{E}$ and because $\text{E}$ is not a smooth manifold- it is known to have conical singularities at each spacetime metric with symmetries. These difficulties are overcome through the use of the dynamic formulation of general relativity as an infinite dimensional Hamiltonian system (ADM formalism) and through the use of constant mean curvature foliations of the spacetimes in $\text{E}$. (We devote considerable space to a review and extension of some special properties of constant mean curvature surfaces and foliations that we need.) The conical singularity structure of $\text{E}$, the sympletic aspects of the ADM formalism, and the uniqueness of constant mean curvature foliations play key roles in the proof of the slice theorem for the action of $\text{D}$ on $\text{E}$. As a consequence of this slice theorem, we find that the space $\text{D}$ = $\text{E}$/$\text{D}$ of gravitational degrees of freedom is a stratified manifold with each stratum being a sympletic manifold. The spaces for homogeneous cosmologies of particular Bianchi types give rise to special finite dimensional symplectic strata in this space $\text{G}$. Our results should extend to such coupled field theories as the Einstein-Yang-Mills equations, since the Yang-Mills system in a given background spacetime admits a slice theorem for the action of the gauge transformation group on the space of Yang-Mills solutions, since there is a satisfactory Hamiltonian treatment of the Einstein-Yang-Mills system, and since the singularity structure of the solution set is known.     

Compactification and supersymmetry in d = 11 supergravity

We examine the conditions under which the ground state of d = 11 supergravity can be supersymmetric and be of the form M⁴ ? B⁷ with M⁴ Minkowski spacetime and B⁷ a compact seven-dimensional manifold. Since we have in mind a background that renders the effective action stationary we make no use of the classical field equations. We find that the requirement that the four-space be flat is very restrictive. It requires all components of the background four-index field to vanish and the compact manifold to be Ricci-flat and hence to have at most the abelian symmetries associated with tori.     

Semiclassical bosonic <Emphasis Type="Italic">D</Emphasis>-brane boundary states in curved spacetime

In this paper we discuss the existence of quantum D-brane states in the strong gravitational field and in the presence of a constant Kalb-Ramond field. A semiclassical string quantization method in which the spacetime metric g _AB and the constant antisymmetric Kalb-Ramond field b _AB are treated exactly is employed. In this framework, the semiclassical D-branes are defined at the first order perturbation around the trajectory of the center-of-mass of a string. The set of equations the semiclassical D-branes must satisfy in a general strong gravitational field are given. These equations are solved in the AdS background where it is shown that a D-brane coherent state exists if the operators that project the string fields onto the corresponding Neumann and Dirichlet directions satisfy a set of algebraic constraints. A second set of equations that should be satisfied by the projectors in order that the semiclassical state be compatible with the global structure of the D-brane are derived in the particle limit of a string in the torsionless AdS background.     

Electromagnetic quasinormal modes of D-dimensional black holes

Using the monodromy method we calculate the asymptotic quasinormal frequencies of an electromagnetic field moving in D-dimensional Schwarzschild and Schwarzschild de Sitter black holes (D ≥ 4). For the D-dimensional Schwarzschild anti-de Sitter black hole we also compute these frequencies with a similar method. Moreover, we calculate the electromagnetic normal modes of the D-dimensional anti-de Sitter spacetime.     

The big bang as a result of the first-order phase transition driven by a change of the scalar curvature in an expanding early Universe: The “hyperinflation” scenario

We suggest that the Big Bang could be a result of the first-order phase transition driven by a change in the scalar curvature of the 4D spacetime in an expanding cold Universe filled with a nonlinear scalar field φ and neutral matter with an equation of state p = νε (where p and ε are the pressure and energy density of the matter, respectively). We consider the Lagrangian of a scalar field with nonlinearity φ⁴ in a curved spacetime that, along with the term–ξR|φ|² quadratic in φ (where ξ is the interaction constant between the scalar and gravitational fields and R is the scalar curvature), contains the term ξRφ₀(φ + φ⁺) linear in φ, where φ₀ is the vacuum mean of the scalar field amplitude. As a consequence, the condition for the existence of extrema of the scalar-field potential energy is reduced to an equation cubic in φ. Provided that ν > 1/3, the scalar curvature R = [κ(3ν–1)ε–4Λ] (where κ and Λ are Einstein’s gravitational and cosmological constants, respectively) decreases with decreasing ε as the Universe expands, and a first-order phase transition in variable “external field” parameter proportional to R occurs at some critical value R _c < 0. Under certain conditions, the critical radius of the early Universe at the point of the first-order phase transition can reach an arbitrary large value, so that this scenario of unrestricted “inflation” of the Universe may be called “hyperinflation.” After the passage through the phase-transition point, the scalar-field potential energy should be rapidly released, which must lead to strong heating of the Universe, playing the role of the Big Bang.     

Gauge invariance for extended objects

Just as the vector potential (one-form) couples to charged point-particles, antisymmetric tensor fields of higher rank (p-forms) couple to elementary objects of higher dimensionality (strings, membranes, …). It is shown that the only possible gauge invariant interaction of such an extended object with a gauge field in spacetime is based on the abelian group U(1). This is unlike the situation for particles where Yang-Mills actions based on any gauge group may be written down. The properties of the abelian theory are explored. It is pointed out that a compact object is analogous to a particle-antiparticle pair and its quantum rate of production in a constant external field is calculated semiclassically. The analysis is performed keeping generic both the dimension of the object and that of spacetime.     

Vacuum charge and the eta function

The vacuum charge of a second quantized spinor field in a static classical background field on a static spacetime is studied. Wheng ₀₀=1 the vacuum charge is shown to be essentially the eta function of the spinor Hamiltonian ats=0. This is computed for compact and noncompact spaces and a boundary dependence is derived in the latter case.     

Übertragung von Polarisation bei sensibilisierenden Stößen angeregter Natriumatome

The transfer of magnetic polarization from state 3p ² p _1/2 to state 3p ² p _3/2 sensitizing collisions of sodium atoms with noble gas atoms has been observed. Sodium atoms were excited by absorption ofD ₁σ⁺-quanta. When buffer gas was added to the sodium vapour, unequal amounts ofD ₂σ⁺ andD ₂σ^? quanta could be detected in the fluorescent light. The difference of the amounts turned out to be proportional to the polarization transferred. The measurement of this difference as a function of the buffer gas pressure provided a method of determining the cross-sections of the polarization transfer. Values of the cross-sections are 22, 24, 26, 20, 23 Ų for the buffer gases He, Ne, Ar, Kr, Xe, respectively. A preliminary investigation shows that the sign of the polarization transferred is reversed when the vapour is exposed to a strong magnetic field acting along the incident light beam.     

Hawking temperature in the eternal BTZ black hole: an example of holography in AdS spacetime

We review the relation between AdS spacetime in 1 $+$ 2 dimensions and the BTZ black hole (BTZbh). Later we show that a ground state in AdS spacetime becomes a thermal state in the BTZbh. We show that this is true in the bulk and in the boundary of AdS spacetime. The existence of this thermal state is tantamount to say that the Unruh effect exists in AdS spacetime and becomes the Hawking effect for an eternal BTZbh. In order to make this we use the correspondence introduced in algebraic holography between algebras of quasi-local observables associated to wedges and double cones regions in the bulk of AdS spacetime and its conformal boundary respectively. Also we give the real scalar quantum field as a concrete heuristic realization of this formalism.     

Aesthetic fields—Null theory

We have studied aesthetic field theory in the case where all invariants constructed from Γ _jk ⁱ and involving g _ij are zero. We studied such a “null” theory in 1972, but the cases we cited were plagued with singularities. By introducing complex fields the situation with respect to singularities improved. Complex fields are consistent with the basic “aesthetic principles” we outlined earlier. Within our null theory we see in two-dimensional spacetime a scattering of particles that was more involved than what we had seen before (regardless of dimensions). We see creation and annihilation of particles out of the vacuum. We also see a three-particle system within a small region of spacetime. In three spacetime dimensions we see a bound two-particle system. Another solution suggests a bound three-particle system. As well as we can tell the particles stay together (confinement) and do not give problems with attenuation. We observe in three dimensions one of the bound systems moving along a definite path in time. The four-dimensional spacetime results are not clear at this point. Whether “topological” bound systems of three particles exist has yet to be determined. A map in the four-dimensional case indicates a planar three maxminima confluence and the suggestion of a second such confluence.     

Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume-Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume-Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h₀/zJ) and (T/zJ, D/zJ), where T absolute temperature, h₀, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z).     

Ghost Dark Energy with Non-Linear Interaction Term

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w _D = p/ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω _D ). We find that in one case, w _D cross the phantom line (w _D < ?1). However in two other classes w _D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w _D , q. We study squared sound speed \({v_{s}^{2}}\), and find that for one case of non-linear interaction term \({v_{s}^{2}}\) can achieves positive values at late time of evolution.     

Search for quantum spacetime foam

The possibility that quantum fluctuations in the structure of spacetime at the Planck scale might be subject to experimental probes in discussed. The effects of spacetime foam in an approach inspired by string theory, in which solitonic D-brane excitations are taken into account when considering the ground state, are studied. The properties of this medium are described by analyzing the recoil of a D particle which is induced by the scattering of a closed-string state. This recoil causes an energy-dependent perturbation of the background metric, which in turn induces an energy-dependent refractive index in vacuo, and stochastic fluctuations of the light cone. Distant astrophysical sources such as Gamma-Ray Bursters (GRBs) may be used to test this possibility, and an illustrative analysis of GRBs whose redshifts have been measured is presented. The propagation of massive particles through such a quantum spacetime foam is also discussed.