We describe static, brane--like, solutions to vacuum Einstein's equations in D = n + m + 2 dimensional spacetime with m \ge 2 and n \ge 1. These solutions have positive ADM mass but no horizon. The curvature invariants are finite everywhere except at r = 0 where r is the radial coordinate in the m + 1 dimensional space. The presence of n \ge 1 extra dimensions is crucial for these properties. Such solutions may be naturally anticipated if Mathur's fuzzball proposal for black holes is correct.
We point out that modern brane theories suffer from a severe vacuum energy problem. To be specific, the Casimir energy associated with the matter fields confined to the brane, is stemming from the one and the same localization mechanism which forms the brane itself, and is thus generically unavoidable. Possible practical solutions are discussed, including in particular spontaneously broken supersymmetry, and quantum mechanically induced brane tension.
We present the study of a two 3-branes system embedded in a 5-dimensional space-time in which the fifth dimension is compacted on a $S^{1}/Z_{2}$ orbifold and the space between the two branes is vacuum. Assuming isotropic and homogeneous space time, we probe that the dynamics of the visible brane is affected by the dynamics of the hidden brane and the possible components which fills it. We study two different cases: assuming a constant equation of state and inflationary scalar field, and its possible consequences in the brane evolution.
We investigate the dynamics of vacuum brane and the bulk in dilatonic brane world. We present exact dynamical solutions which describe the vacuum dilatonic brane world. We find that the solution has initial singularity and singularity at spatial infinity.
We study the cosmology of a two-brane model in a five-dimensional spacetime, where the extra spatial coordinate is compactifed on an orbifold. Additionally, we consider the existence on each brane of matter fields that evolve in time. Solving the Einstein equations in a vacuum bulk, we can show how the matter fields in both branes are connected and they do not evolve independently
We consider some classes of solutions of the static, spherically symmetric gravitational field equations in the vacuum in the brane world scenario, in which our Universe is a three-brane embedded in a higher dimensional space-time. The vacuum field equations on the brane are reduced to a system of two ordinary differential equations, which describe all the geometric properties of the vacuum as functions of the dark pressure and dark radiation terms (the projections of the Weyl curvature of the bulk, generating non-local brane stresses). Several classes of exact solutions of the vacuum gravitat…
The enhancement in the decay rate of the Kaluza-Klein vacuum due to the presence of a brane is studied, both in the test brane approximation and beyond it. Spontaneous brane materialization in the Kaluza-Klein vacuum is also described.
We construct solutions in purely gravitational bulk with flat vacuum branes without fine tuning the constants of the theory. Our solutions incorporate one or two branes and have topology S^1 x R^4 without Z_2 symmetry. They are not invariant under the four-dimensional Lorentz group effectively acting on the brane, but the significance of this fact will become clear only after the study of their perturbations.
Vacuum expectation value of the energy-momentum tensor and the vacuum interaction forces are evaluated for a massive scalar field with general curvature coupling parameter satisfying Robin boundary conditions on two codimension one parallel branes embedded in background spacetime $AdS_{D_1+1}\times Σ$ with a warped internal space $Σ$. The vacuum energy-momentum tensor is presented as a sum of boundary-free, single brane induced, and interference parts. The latter is finite everywhere including the points on the branes and is exponentially small for large interbrane distances. Unlike to the pur…
We investigate the combined effects of a magnetic flux-carrying cosmic string and a brane on the fermionic condensate (FC) and on the vacuum expectation value (VEV) of the energy-momentum tensor for a massive charged fermionic field in background of 5-dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and it divides the space into two regions with distinct properties of the fermionic vacuum. For two types of boundary conditions on the field operator and for the fields realizing two inequivalent representations of the Clifford algebra, the brane-induced contri…
The fermionic one loop vacuum energy of the superstring theory in a system of non-parallel D1-branes is derived by applying the path integral formalism.
We investigate the effects of a brane and magnetic-flux-carrying cosmic string on the vacuum expectation value (VEV) of the current density for a charged fermionic field in the background geometry of 4+1 dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the cosmic string is orthogonal to the brane. Two types of boundary conditions are considered on the brane that include the MIT bag boundary condition and the boundary conditions in Z2-symmetric braneworld models. The brane divides the space into two regions with different properties of the vacuum state. …
We discuss the vacuum energy density and the cosmological constant of dS$_5$ brane world with a dilaton field. It is shown that a stable AdS$_4$ brane can be constructed and gravity localization can be realized. An explicit relation between the dS bulk cosmological constant and the brane cosmological constant is obtained. The discrete mass spectrum of the massive scalar field in the AdS$_4$ brane is used to acquire the relationship between the brane cosmological constant and the vacuum energy density. The vacuum energy density in the brane gotten by this method is in agreement with astronomica…
In this paper we analyse the vacuum polarization effects associated with a massless scalar field in the higher-dimensional spacetime. Specifically we calculate the renormalized vacuum expectation value of the square of the field, $<Φ^2(x)>_{Ren}$, induced by a global monopole in the "braneworld" scenario. In this context the global monopole lives in a $n=3$ dimensional sub-manifold of the higher-dimensional (bulk) spacetime, and our Universe is represented by a transverse flat $(p-1)-$ dimensional brane. In order to develop this analysis we calculate the general Green function admitting that t…
I point out a symmetry, between equations of state for polytropic fluids, in the equation of motion of a spherically symmetric singular shell embedded in 4-d and 5-d vacuum spacetimes. In particular the equation of motion of a shell consisting of radiation has the same form as for a vacuum shell or domain wall.
We investigate the Wightman function, the mean field squared and the vacuum expectation values of energy-momentum tensor for a scalar field in AdS spacetime, in the presence of a brane perpendicular to the AdS boundary. On the brane the field operator obeys Robin boundary condition. The vacuum expectation values are decomposed into the boundary-free AdS and brane-induced contributions. In this way, for points away from the brane, the renormalization is reduced to the one in pure AdS spacetime. It is shown that at proper distances from the brane larger than the AdS curvature radius the brane-in…
In the present paper, we give some theorems representing ridigity of a vacuum brane in static bulk spacetimes. As an application, we show that a static bulk spacetime with dimension D>3 and spatial symmetry IO(D-2), O(D-1) or O_+(D-2,1) does not allow a vacuum brane with a black hole on it. We also show that if a static bulk spacetime with dimension D>4 satsifying the vacuum Einstein equations can be foliated by a continuous family of vacuum branes with asymptotically constant curvature, it is a black string solution.
Vacuum expectation values of the surface energy-momentum tensor is investigated for a massless scalar field obeying mixed boundary condition on a brane in de Sitter bulk. To generate the corresponding vacuum surface densities we use the conformal relation between de Sitter and Rindler spacetimes.
Wightman function and vacuum expectation value of the field square are evaluated for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two codimension one parallel branes located on $(D+1)$-dimensional background spacetime $AdS_{D_1+1}\times Σ$ with a warped internal space $Σ$. The general case of different Robin coefficients on separate branes is considered. The application of the generalized Abel-Plana formula for the series over zeros of combinations of cylinder functions allows us to extract manifestly the part due to the bulk without …
For a massive scalar field with general curvature coupling parameter we evaluate Wightman function, vacuum expectation values of the field square and the energy-momentum tensor induced by a $Z_{2}$-symmetric brane with finite thickness located on $(D+1)$-dimensional AdS bulk. For the general case of static plane symmetric interior structure the expectation values in the region outside the brane are presented as the sum of free AdS and brane induced parts. For a conformally coupled massless scalar the brane induced part in the vacuum energy-momentum tensor vanishes. In the limit of strong gravi…
We calculate vacuum energy for twisted SUSY D-brane on toroidal background with constant magnetic or constant electric field. Its behaviour for toroidal D-brane (p=2) in constant electric field shows the presence of stable minimum for twisted versions of the theory. That indicates such a background maybe reasonable groundstate.
We consider tachyonic string-field fluctuations about a Dp-brane background in the geometrical (CFT) formulation of Vacuum String Field Theory. We then extend this analysis to the case of a background B-field. We find that the standard results for D-brane tension are reproduced in both cases.
We consider a spherical thick 3-brane immersed in a five-dimensional bulk spacetime. We demonstrate how the thick brane equation of motion expanded in powers of the thickness of the brane can be obtained from the expected junction conditions on the boundaries of thick brane with the two embedding spacetimes. It is shown that the finite thickness leads to a faster collapse of the spherical shell.
We give a short review of the recent development in the investigation of the vacuum expectation values of the bulk and surface energy-momentum tensors generated by quantum fluctuations of a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two codimension one parallel branes located on $(D+1)$-dimensional anti-de Sitter (AdS) bulk. An application to the Randall-Sundrum braneworld with arbitrary mass terms on the branes is discussed.
Positive frequency Wightman function, vacuum expectation values of the field square and the energy-momentum tensor induced by a Z_{2}-symmetric brane with finite thickness located on (D+1)- dimensional AdS background are evaluated for a massive scalar field with general curvature coupling parameter. For the general case of static plane symmetric interior structure the expectation values in the region outside the brane are presented as the sum of free AdS and brane induced parts. For a conformally coupled massless scalar the brane induced part in the vacuum energy-momentum tensor vanishes. In t…
In the context of colliding brane worlds I discuss a toy cosmological model, developed in collaboration with E. Gravanis, which arguably produces inflation and a relaxing to zero cosmological ``constant'' hierarchically small as compared to the supersymmetry breaking (TeV) scale. Supersymmetry breaking is induced by compactification of the brane worlds on magnetized tori. The crucial ingredient is the non-criticality (non conformality) of string theory on the observable brane world induced at the collision, which is thus viewed as a cause for departure from equilibrium in this system. The hier…
A massive scalar field is quantized in the background of a cosmic string which is generalized to a static flux-carrying codimension-2 brane in the locally flat multidimensional space-time. We find that the finite energy-momentum tensor is induced in the vacuum. The dependence of the tensor components on the brane flux and tension, as well as on the coupling to the space-time curvature scalar, is comprehensively analyzed. The tensor components are holomorphic functions of space dimension, decreasing exponentially with the distance from the brane. The case of the massless quantized scalar field …
Following Polchinski's approach we calculate the one-loop vacuum amplitude for two parallel D-branes connected by open bosonic (neutral or charged)string in a constant uniform electromagnetic (EM) field. For neutral string, external EM field contribution appears as multiplier (Born-Infeld type action) of vacuum amplitude without external EM field. Hence,it gives the alternative way to see the inducing of Born-Infeld type action for description of D-branes. For charged string the situation is more complicated, it may indicate the necessity to modify the induced D-branes action in this case.
We evaluate the Hadamard function and the vacuum expectation value (VEV) of the current density for a charged scalar field in the region between two co-dimension one branes on the background of locally AdS spacetime with an arbitrary number of toroidally compactified spatial dimensions. Along compact dimensions periodicity conditions are considered with general values of the phases and on the branes Robin boundary conditions are imposed for the field operator. In addition, we assume the presence of a constant gauge field. The latter gives rise to Aharonov-Bohm type effect on the vacuum current…
We analyze the stability of the structure equations of the vacuum in the brane world models, by using both the linear (Lyapunov) stability analysis, and the Jacobi stability analysis, the Kosambi-Cartan-Chern (KCC) theory. In the brane world models the four dimensional effective Einstein equations acquire extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the 3-brane in the bulk. Generally, the spherically symmetric vacuum solutions of the brane gravitational field equations, have properties quite distinct as compared to the standard black hol…
We study the vacuum polarization of supersymmetric toroidal D-brane placed in the constant electromagnetic field. Explicit calculation of the one-loop effective potential is performed for membrane with constant magnetic or electric background. We find the one-loop potentials vanish as the effect of supersymmetry,
For a massive scalar field with general curvature coupling we evaluate the Wightman function in the geometry of two parallel branes perpendicular to the AdS boundary. On the separate branes, the field operator is constrained by Robin boundary conditions, in general, with different coefficients. In the region between the branes their contribution to the Wightman function is explicitly separated. By using this decomposition, the brane-induced effects on the vacuum expectation values (VEVs) for the field squared and energy-momentum tensor are investigated. The behavior of those expectation values…
Branes with constant mean curvature of their hyper-worldsheets of codim 1 are treated as the Nambu-Goldstone fields of the broken Poincare symmetry. Mapping of their action into quadratic curvature gravity action with spontaneously generated gravity, is shown. Equation for the brane potential extremals and its solution describing hyper-ws of constant curvature are found. For membranes in $\mathbf{R}^{1,3}$ this extremum is shown to be a saddle 3-dim. hypersurface which defines classically unstable vacuum.
We obtain axionic charged primordial black holes on a vacuum created gravitational pair of $(3{\bar 3})$-brane by the Kalb-Ramond field on a $D_4$-brane in presence of a background open string metric. The new geometries on an emergent pair of $(3{\bar 3})$-brane universe is shown to be influenced by the non-perturbative quantum effects underlying a geometric torsion in a second order formalism. The presence of small extra dimensions transverse to the pair in the formalism ensures dynamical scalar fields hidden to a $3$-brane or an anti 3-brane universe. We investigate the non-perturbative quan…
In the framework of the Sen conjectures a construction of vacuum superstring field theory on a non-BPS brane is discussed. A distinguished feature of this theory is a presence of a ghost kinetic operator mixing GSO+/- sectors. A candidate for such kinetic operator with zero cohomology is discussed.
In this paper, we give a complete classification of vacuum branes, i.e., everywhere umbilical time-like hypersurfaces whose extrinsic curvature is a constant multiple of the induced metric, K_mn=k g_mn, in D-dimensional static spacetimes with spatial symmetry G(D-2,K), where G(n,K) is the isometry group of an n-dimensional space with constant sectional curvature K. D>=4 is assumed. It is shown that all possible configurations of a brane are invariant under an isometry subgroup G(D-3,K') for some K'>= K. In particular, configurations of a brane with non-zero k are always G(D-2,K) invariant, exc…
We review the results of investigations for brane-induced effects on the local properties of quantum vacuum in background of AdS spacetime. Two geometries are considered: a brane parallel to the AdS boundary and a brane intersecting the AdS boundary. For both these cases the contribution in the vacuum expectation value (VEV) of the energy-momentum tensor is separated explicitly and its behavior in various asymptotic regions of the parameters is studied. It is shown that the influence of the gravitational field on the local properties of the quantum vacuum is essential at distance from the bran…
Charged scalar field is quantized in the background of a static d-2 - brane which is a core of the magnetic flux lines in flat d+1 - dimensional space-time. We find that vector potential of the magnetic core induces the energy-momentum tensor in the vacuum. The tensor components are periodic functions of the brane flux and holomorphic functions of space dimension. The dependence on the distance from the brane and on the coupling to the space-time curvature scalar is comprehensively analysed.
A geometric torsion dynamics leading to an effective curvature in a second order formalism on a D4-brane is revisited with a renewed interest. We obtain two effective $AdS_4$ brane geometries on a vacuum created pair of $(D{\bar D})_3$-brane. One of them is shown to describe an AdS Schwarzschild spinning black hole and the other is shown to describe a spinning black hole bound state. It is argued that a D-instanton in a vacuum created anti D3-brane within a pair may describe a quintessence. It may seen to incorporate a varying vacuum energy density in a brane universe. We consider the effectiv…
We introduce a new brane-world model in which the bulk solution consists of outgoing plane waves. This is an exact solution to string theory with no naked singularities. The recently discussed self-tuning mechanism to cancel the cosmological constant on a brane is naturally incorporated. We show that even if the vacuum energy on the brane changes, e.g. due to a phase transition, the brane geometry remains insensitive to the local vacuum energy. We also consider the static self-tuning branes introduced earlier, and find a solution in which the brane geometry starts to contract when the vacuum e…
We show that many of the recently proposed supersymmetric p-brane solutions of d=10 and d=11 supergravity have the property that they interpolate between Minkowski spacetime and a compactified spacetime, both being supersymmetric supergravity vacua. Our results imply that the effective worldvolume action for small fluctuations of the super p-brane is a supersingleton field theory for $(adS)_{p+2}$, as has been often conjectured in the past.
Non-extremal overlapping p-brane supergravity solutions localised in their relative transverse coordinates are constructed. The construction uses an algebraic method of solving the bosonic equations of motion. It is shown that these non-extremal solutions can be obtained from the extremal solutions by means of the superposition of two deformation functions defined by vacuum solutions of M-theory. Vacuum solutions of M-theory including irrational powers of harmonic functions are discussed.
We analyze the process of string vacuum destabilization due to instanton induced superpotential couplings which depend linearly on charged fields. These non-perturbative instabilities result in potentials for the D-brane moduli and lead to processes of D-brane recombination, motion and partial moduli stabilization at the non-perturbative vacuum. By using techniques of D-brane instanton calculus, we explicitly compute this scalar potential in toroidal orbifold compactifications with magnetized D-branes by summing over the possible discrete instanton configurations. We illustrate explicitly the …
We discuss the effects from the Kaluza-Klein modes in the brane world scenario when an interaction between bulk and brane fields is included. We focus on the bulk inflaton model, where a bulk field $Ψ$ drives inflation in an almost $AdS_5$ bulk bounded by an inflating brane. We couple $Ψ$ to a brane scalar field $ϕ$ representing matter on the brane. The bulk field $Ψ$ is assumed to have a light mode, whose mass depends on the expectation value of $ϕ$. To estimate the effects from the KK modes, we compute the 1-loop effective potential $V_\eff(ϕ)$. With no tuning of the parameters of the model,…
A non-local classical duality between the three-block truncated 11D supergravity and the 8D vacuum gravity with two commuting Killing symmetries is established. The supergravity four-form field is generated via an inverse dualisation of the corresponding Killing two-forms in six dimensions. 11D supersymmetry condition is shown to be equivalent to existence of covariantly constant spinors in eight dimensions. Thus any solution to the vacuum Einstein equations in eight dimensions depending on six coordinates and admitting Killing spinors have supersymmetric 11D-supergravity counterparts. Using t…
We find the classical supersymmetric vacuum states of a class of N = 1* field theories obtained by mass deforming superconformal models with simple gauge groups and N = 4 or N =2 supersymmetry. In particular, new classical vacuum states for mass-deformed N = 4 models with Sp(2N) and SO(N) gauge symmetry are found. We also derive the classical vacua for various mass-deformed N=2 models with Sp(2N) and SU(N) gauge groups and antisymmetric (and symmetric) hypermultiplets. We suggest interpretations of the mass-deformed vacua in terms of three-branes expanded into five-brane configurations.
The fermion representations and boundary conditions in five dimensional anti de Sitter space are described in detail. In each case the one loop effective action is calculated for massless fermions. The possibility of topological or Wilson loop symmetry breaking is discussed.
The minimal geometric deformation approach is employed to show the existence of brane-world stellar distributions with vacuum Schwarzschild exterior, thus without energy leaking from the exterior of the brane-world star into the extra dimension. The interior satisfies all elementary criteria of physical acceptability for a stellar solution, namely, it is regular at the origin, the pressure and density are positive and decrease monotonically with increasing radius, finally all energy conditions are fulfilled. A very thin solid crust with negative radial pressure separates the interior from the …
We investigate charged dilatonic black $p$-branes smeared on a transverse circle. The system can be reduced to neutral vacuum black branes, and we perform static perturbations for the reduced system to construct non-uniform solutions. At each order a single master equation is derived, and the Gregory-Laflamme critical wavelength is determined. Based on the non-uniform solutions, we discuss thermodynamic properties of this system and argue that in a microcanonical ensemble the non-uniform smeared branes are entropically disfavored even near the extremality, if the spacetime dimension is $D \le …
The vacuum expectation value (VEV) of the fermionic current density is investigated in the geometry of two parallel branes in locally AdS spacetime with a part of spatial dimensions compactified to a torus. Along the toral dimensions quasiperiodicity conditions are imposed with general phases and the presence of a constant gauge field is assumed. Different types of boundary conditions are discussed on the branes, including the bag boundary condition and the conditions arising in $Z_{2}$-symmetric braneworld models. Nonzero vacuum currents appear along the compact dimensions only. In the region…
A sliver state is a classical solution of the string field theory of the tachyon vacuum that represents a background with a single D25-brane. We show that the sliver wavefunctional factors into functionals of the left and right halves of the string, and hence can be naturally regarded as a rank-one projector in a space of half-string functionals. By developing an algebraic oscillator approach we are able construct higher rank projectors that describe configurations of multiple D-branes of various dimensionalities and located at arbitrary positions. The results bear remarkable similarities with…
The two-point function and VEV of the current density are investigated for a massive charged scalar field with arbitrary curvature coupling in the geometry of a brane on background of AdS spacetime with partial toroidal compactification.The presence of a gauge field flux enclosed by compact dimensions is assumed.On the brane the field obeys Robin boundary condition and along compact dimensions periodicity conditions with general phases are imposed.There is a range in the space of values for the coefficient in the boundary condition where Poincare vacuum is unstable.This range depends on the br…
The Randall-Sundrum two-brane model admits the flat-brane Lorentz-invariant vacuum solution only if the branes have exactly opposite tensions. We pay attention to this condition and propose a generalization of this model in which two branes are described by actions of the same form and with the same matter content but {\em with opposite signs}. In this way, the relation between their tensions (which are their vacuum energy densities) is naturally accounted for. We study a simple example of such a model in detail. It represents the Randall-Sundrum model supplemented by the Einstein scalar-curva…
We first recall a covariant formalism used to compute conserved charges in gauge invariant theories. We then study the case of gravity for two different boundary conditions, namely spatial infinity and a Brane-World boundary. The new conclusion of this analysis is that the gravitational energy (and linear and angular momentum) is a local expression if our universe is really a boundary of a five-dimensional spacetime.
We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD brane-world scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperatur…
In this paper we investigate the vacuum energies of several models of quantum fields interacting with static external currents (linear couplings) concentrated along parallel branes with an arbitrary number of codimensions. We show that we can simulate the presence of static charges distributions as well as the presence of classical static dipoles in any dimension for massive and massless fields. We also show that we can produce confining potentials with massless self interacting scalar fields as well as long range anisotropic potentials.
Classical superstring vacua have zero vacuum energy and are supersymmetric and Lorentz-invariant. We argue that all these properties may be destroyed when quantum aspects of the interactions between particles and non-perturbative vacuum fluctuations are considered. A toy calculation of string/D-brane interactions using a world-sheet approach indicates that quantum recoil effects - reflecting the gravitational back-reaction on space-time foam due to the propagation of energetic particles - induce non-zero vacuum energy that is linked to supersymmetry breaking and breaks Lorentz invariance. This…
