Negative Tension Brane Research Articles

Multigravity in six dimensions: Generating bounces with flat positive tension branes

We present a generalization of the five dimensional multigravity models to six dimensions. The key characteristic of these constructions is that that we obtain solutions which do not have any negative tension branes while at the same time the branes are kept flat. This is due to the fact that in six dimensions the internal space is not trivial and its curvature allows bounce configurations with the above feature. These constructions give for the first time a theoretically and phenomenologically viable realization of multigravity.

COSMOLOGY AND HIERARCHY IN STABILIZED RANDALL-SUNDRUM MODELS

We consider the cosmology and hierarchy of scales in models with immersed in a five-dimensional curved spacetime subject to radion stabilization. The universe naturally find itself in the radiation-dominated epoch when the inter-brane spacing is static and stable, independent of the form of the stabilizing potential. We recover the standard Friedmann equations without assuming a specific form for the bulk energy-momentum tensor. We address the hierarchy problem in the context of a quartic and exponential stabilizing potential, and find that in either case the presence of a negative tension brane is required and that the string scale can be as low as the electroweak scale. In the situation of self-tuning branes (corresponding to an exponential potential) where the bulk cosmological constant is set to zero, the brane tensions have hierarchical values.

Black holes and instabilities of negative tension branes

We consider the collision in $2+1$ dimensions of a black hole and a negative tension brane on an orbifold. Because there is no gravitational radiation in $2+1$ dimensions, the horizon area shrinks when part of the brane falls through. This provides a potential violation of the generalized second law of thermodynamics. However, tracing the details of the dynamical evolution, one finds that it does not proceed from equilibrium configuration to equilibrium configuration. Instead, a catastrophic space-time singularity develops similar to the ``big crunch'' of $\ensuremath{\Omega}>1$ Friedmann-Robertson-Walker space-times. In the context of classical general relativity, our result demonstrates the instability of constructions with negative tension branes.

New formulations of D = 10 supersymmetry and D8-O8 domain walls

We discuss a generalized form of IIA/IIB supergravity depending on all R-R potentials C(p) (p = 0,1,...,9) as the effective field theory of type IIA/IIB superstring theory. For the IIA case we explicitly break this R-R democracy to either p⩽3 or p⩾5, which allows us to write a new bulk action that can be coupled to N = 1 supersymmetric brane actions. The case of eight-branes is studied in detail using the new bulk & brane action. The supersymmetric negative-tension branes without matter excitations can be viewed as orientifolds in the effective action. These D8-branes and \\mbox{O$8$-planes} are fundamental in type I' string theory. A BPS eight-brane solution is given which satisfies the jump conditions on the wall. It implies a quantization of the mass parameter in string units. Also, we find a maximal distance between the two walls, depending on the string coupling and the mass parameter. We derive the same results via supersymmetric flow equations.

Consistency conditions for brane worlds in arbitrary dimensions

We consider ``brane world sum rules'' for compactifications involving an arbitrary number of spacetime dimensions. One of the most striking results derived from such consistency conditions is the necessity for negative tension branes to appear in five--dimensional scenarios. We show how this result is easily evaded for brane world models with more than five dimensions. As an example, we consider a novel realization of the Randall--Sundrum scenario in six dimensions involving only positive tension branes.

(De)stabilization of an extra dimension due to a Casimir force

We study the stabilization of one spatial dimension in (p+1+1)-dimensional spacetime in the presence of $p$-dimensional brane(s), a bulk cosmological constant and the Casimir force generated by a conformally coupled scalar field. We find general static solutions to the metric which require the fine-tuning of the inter-brane distance and the bulk cosmological constant (leaving the two brane tensions as free parameters) corresponding to a vanishing effective cosmological constant and a constant radion field. Taking these solutions as a background configuration, we perform a dimensional reduction and study the effective theory in the case of one- and two-brane configurations. We show that the radion field can have a positive mass squared, which corresponds to a stabilization of the extra dimension, only for a repulsive nature of the Casimir force. This type of solution requires the presence of a negative tension brane. The solutions with one or two positive tension branes arising in this theory turn out to have negative radion mass squared, and therefore are not stable.

BIG BANG IN AdS5 WITH EXTERNAL FIELD AND FLAT 4d UNIVERSE

We describe the spontaneous creation of the brane world in AdS 5 with external field. The resulting brane world consists of a flat 4d spatially finite expanding universe and curved expanding "regulator" branes. No negative tension branes are involved.

Static solutions in theR4brane world

A simple five-dimensional brane world model is proposed, motivated by M theory compactified on a six-dimensional manifold of small radius and an ${S}^{1}{/Z}_{2}$ of large radius. We include a leading-order higher curvature correction to the tree-level bulk action since in brane world scenarios the curvature scale in the bulk may be comparable to the five-dimensional Planck scale and, thus, higher curvature corrections may become important. As a tractable model of the bulk theory we consider pure gravity including a ${(\mathrm{R}\mathrm{i}\mathrm{c}\mathrm{c}\mathrm{i}\ensuremath{-}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{r})}^{4}$ correction to the Einstein-Hilbert action. In this model theory, after a conformal transformation to the Einstein frame, we numerically obtain static solutions, each of which consists of a positive tension brane and a negative tension brane. For these solutions, we obtain two relations between the warp factor and the brane tensions. The existence of these relations implies that, contrary to the original Randall-Sundrum model, the so called radion is no longer a zero mode. We conclude that the tension of our brane should be negative and that fine-tuning of the tension of both branes is necessary for a large warp factor to explain the large hierarchy between the Planck scale and the electroweak scale.

A new bigravity model with exclusively positive branes

We propose a new “bigravity” model with two positive tension AdS 4 branes in AdS 5 bulk and no negative tension branes. The bounce of the “warp” factor mimics the effect of a negative brane and thus gives rise to an anomalously light graviton KK mode. This configuration satisfies the weak energy condition and has no ghost state. In addition, the extra polarization states of the massive graviton practically decouple and thus it does not contradict to Einsteinian gravity. However, the model has certain phenomenological difficulties associated with the presence of a negative cosmological constant on the branes.

Multibrane worlds and modification of gravity at large scales

We discuss the implications of multibrane constructions involving combinations of positive and negative tension brane and show how anomalously light KK states emerge when negative tension “ − ” branes are sandwiched between “ + ” branes. We present a detailed study of a “ +−−+ ” brane assignment which interpolates between two models that have been previously proposed in which gravity is modified at large scales due to the anomalously light states. We show that it has the peculiar characteristic that gravity changes from four-dimensional (4D) to 5D at large distances and returns to 4D at even larger scales. We also consider a crystalline universe which leads to a similar structure for gravity. The problems associated with intermediate negative tension branes are discussed and a possible resolution suggested.

The μ and soft masses from the intermediate scale brane with non-factorizable geometry

The proton decay problem and the negative brane tension problem in the original Randall–Sundrum model can be resolved by interpreting the Planck scale brane as the visible sector brane. The hierarchy problem is resolved with supersymmetry, and the TeV scales for soft masses and μ in supersymmetric models are generated by the physics at the intermediate scale (∼10 11–13 GeV) brane.

Supersymmetry in singular spaces

We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D=5 and comment on 8-branes in D=10. The new construction has an interpretation that the brane is a sink for the flux and requires adding to the standard supergravity a (D-1)-form field and a supersymmetry singlet field. This allows a consistent definition of supersymmetry on a S_1/Z_2 orbifold, the bulk and the brane actions being separately supersymmetric. Randall-Sundrum brane-worlds can be reproduced in this framework without fine tuning. For fixed scalars, the doubling of unbroken supersymmetries takes place and the negative tension brane can be pushed to infinity. In more general BPS domain walls with 1/2 of unbroken supersymmetries, the distance between branes in some cases may be restricted by the collapsing cycles of the Calabi-Yau manifold. The energy of any static x^5-dependent bosonic configuration vanishes, E=0, in analogy with the vanishing of the Hamiltonian in a closed universe.

A note on brane inflation

We demonstrate that there exists an inflationary solution on the positive tension brane in the Randall-Sundrum scenario. Inflation is driven by a slow-rolling scalar field on the brane and is achieved within the perturbative limit of the radion field. We find that inflation on the positive tension brane results in a slight increase in the separation between the two branes. However, we show that the slow-roll inflation is not possible on the negative tension brane.

On stability of the three 3-brane model

We show that the Goldberger-Wise mechanism for the three 3-brane scenario proposed by Kogan et al. stabilizes the radion. We find that the system of 3-branes stabilizes in such a way that the loss in the scale factor is insignificant. That is, the negative tension brane chooses to stay close to the visible brane.

Brane surgery: energy conditions, traversable wormholes, and voids

Branes are ubiquitous elements of any low-energy limit of string theory. We point out that negative tension branes violate all the standard energy conditions of the higher-dimensional spacetime they are embedded in; this opens the door to very peculiar solutions of the higher-dimensional Einstein equations. Building upon the (3+1)-dimensional implementation of fundamental string theory, we illustrate the possibilities by considering a toy model consisting of a (2+1)-dimensional brane propagating through our observable (3+1)-dimensional universe. Developing a notion of "brane surgery", based on the Israel--Lanczos--Sen "thin shell" formalism of general relativity, we analyze the dynamics and find traversable wormholes, closed baby universes, voids (holes in the spacetime manifold), and an evasion (not a violation) of both the singularity theorems and the positive mass theorem. These features appear generic to any D-brane model that permits negative tension branes: This includes the Randall--Sundrum models and their variants.

Universal aspects of gravity localized on thick branes

We study gravity in backgrounds that are smooth generalizations of the Randall-Sundrum model, with and without scalar fields. These generalizations include three-branes in higher dimensional spaces which are not necessarily Anti-de Sitter far from the branes, intersecting brane configurations and configurations involving negative tension branes. We show that under certain mild assumptions there is a universal equation for the gravitational fluctuations. We study both the graviton ground state and the continuum of Kaluza-Klein modes and we find that the four-dimensional gravitational mode is localized precisely when the effects of the continuum modes decouple at distances larger than the fundamental Planck scale. The decoupling is contingent only on the long-range behaviour of the metric from the brane and we find a universal form for the corrections to Newton's Law. We also comment on the possible contribution of resonant modes. Given this, we find general classes of metrics which maintain localized four-dimensional gravity. We find that three-brane metrics in five dimensions can arise from a single scalar field source, and we rederive the BPS type conditions without any a priori assumptions regarding the form of the scalar potential. We also show that a single scalar field cannot produce conformally-flat locally intersecting brane configurations or a p-brane in greater than (p+2)-dimensions.

Cosmology and hierarchy in stabilized warped brane models

We examine the cosmology and hierarchy of scales in models with branes immersed in a five-dimensional curved spacetime subject to radion stabilization. When the radion field is time-independent and the inter-brane spacing is stabilized, the universe can naturally find itself in the radiation-dominated epoch. This feature is independent of the form of the stabilizing potential. We recover the standard Friedmann equations without assuming a specific form for the bulk energy-momentum tensor. In the models considered, if the observable brane has positive tension, a solution to the hierarchy problem requires the presence of a negative tension brane somewhere in the bulk. We find that the string scale can be as low as the electroweak scale. In the situation of self-tuning branes where the bulk cosmological constant is set to zero, the brane tensions have hierarchical values. In the case of a polynomial stabilizing potential no new hierarchy is created.

The fate of the radion in models with metastable graviton

We clarify some general issues in models where gravity is localized at intermediate distances. We introduce the radion mode, which is usually neglected, and we point out that its role in the model is crucial. We show that the brane bending effects discussed in the literature can be obtained in a formalism where the physical origin is manifest. The model violates positivity of energy due to a negative tension brane, which induces a negative kinetic term for the radion. The very same effect that violates positivity is responsible for the recovery of conventional Einstein gravity at intermediate distances.

Brane universe and multigravity: modification of gravity at large and small distances

We consider the modification of gravity at large distances in Brane Universes which was discussed recently [I.I. Kogan, S. Mouslopoulos, A. Papazoglou, G.G. Ross, J. Santiago, hep-ph/9912552; R. Gregory, V.A. Rubakov, S.M. Sibiryakov, hep-th/0002072; C. Csaki, J. Erlich, T.J. Hollowood, hep-th/0002161; G. Dvali, G. Gabadadze, M. Porrati, hep-th/0002190]. In these models the modification of gravity at large distances is connected to the existence of a negative tension brane(s) and an exponentially small tunneling factor. We discuss a general model which interpolates between the Bi-gravity +−+ model [I.I. Kogan, S. Mouslopoulos, A. Papazoglou, G.G. Ross, J. Santiago, hep-ph/9912552] and the GRS model [R. Gregory, V.A. Rubakov, S.M. Sibiryakov, hep-th/0002072]. We also discuss the possible mechanism of stabilization of negative tension branes in an AdS background. Finally we show that extra degrees of freedom of massive gravitons do not lead to a disastrous contradiction with General Relativity if the stabilization condition ∫ dy −G (5) (T μ μ−2T 5 5)=0 [P. Kanti, I.I. Kogan, K.A. Olive, M. Pospelov, hep-ph/9912266] is implemented.

Scalar-tensor gravity in a two 3-brane system

We derive the low-energy effective action of four-dimensional gravity in the Randall-Sundrum scenario in which two 3-branes of opposite tension reside in a five-dimensional spacetime. The dimensional reduction with the Ansatz for the radion field of Charmousis, Gregory, and Rubakov, which solves five-dimensional linearized field equations, results in a class of scalar-tensor gravity theories. In the limit of vanishing radion fluctuations, the effective action reduces to the Brans-Dicke gravity in accord with the results of Garriga and Tanaka: Brans-Dicke gravity with the corresponding Brans-Dicke parameter $0<\ensuremath{\omega}<\ensuremath{\infty}$ (for positive tension brane) and $\ensuremath{-}3/2<\ensuremath{\omega}<0$ (for negative tension brane). In general the gravity induced brane belongs to a class of scalar-tensor gravity with the Brans-Dicke parameter which is a function of the interval and the radion. In particular, gravity on a positive tension brane contains an attractor mechanism toward the Einstein gravity.