In the warped space model, the inter-brane distance can be stabilized by the Goldberger-Wise mechanism. Of particular importance, the stabilization potential calls for a proper identification of the dynamical degree of freedom. In this paper, we provided a complete calculation of the effective Lagrangian till the quadratic order that is generic for the Randall-Sundrum model and its $N$-brane $(N \geq 4)$ extensions. By applying the variation principle to a specific perturbation field, we derived the equations of motion and orthogonal conditions for decoupling the graviton. This approach is demonstrated to be equivalent to the analysis using the linearized Einstein equation. Our derivation clarifies that in the $N$-brane set up, just one degree of freedom for the radion field is dynamical, with the other modes eliminated by the gauge fixings. Thus we can directly generalize the GW stabilization to the $N$-brane model in a way similar to the RS1 scenario.
We study various aspects of warped conformal field theories (WCFTs) in two dimensions. We find new Lagrangian WCFTs, and show that all known Lagrangian WCFTs are local only after an infinite tuning. We deduce the anomalies of WCFTs and relate them to central charges, as well as analyze WCFT hydrostatics, thereby re-deriving the warped analogue of the Cardy formula. Finally, we point out that holographic WCFTs are semi-local, that matter fields in spacelike WAdS$_3$ black hole geometries exhibit a Gregory-Laflamme-like instability, and that WAdS$_3$ throats do not admit a decoupling limit.
We generalize the Randall Sundrum warped braneworld model in six and higher dimension and propose a resolution to the mass hierarchy among the standard model fermions. The fine tuning problem in connection with the scalar mass however is shown to reappear in a new guise in five dimensional warped model when the two form antisymmetric tensor fields, a massless string mode, propagates in the bulk. Finally the issue of modulus stabilization is re-examined in presence of a bulk scalar by considering it's back-reaction on the background geometry. The role of higher derivative term of the bulk scala…
We study the thermodynamic stability of warped black holes in three-dimensional topologically massive gravity. The spacelike stretched black hole is parametrized by its mass and angular momentum. We determine the local and global stability properties in the canonical and grand canonical ensembles. The presence of a Hawking-Page type transition is established, and the critical temperature is determined. The thermodynamic metric of Ruppeiner is computed, and the curvature is shown to diverge in the extremal limit. The consequences of these results for the classical stability properties of warped…
We show the dynamical stability of a six-dimensional braneworld solution with warped flux compactification recently found by the authors. We consider linear perturbations around this background spacetime, assuming the axisymmetry in the extra dimensions. The perturbations are expanded by scalar-, vector- and tensor-type harmonics of the four-dimensional Minkoswki spacetime and we analyze each type separately. It is found that there is no unstable mode in each sector and that there are zero modes only in the tensor sector, corresponding to the four-dimensional gravitons. We also obtain the firs…
We investigate the stability of a new warped black string with nontrivial topologies in five-dimensional Anti-de Sitter spacetime. After studying the linear gravitational perturbation, we find that this black string is unstable when the Kaluza-Klein mass falls in a certain range and the instability exists for all topological spacetimes.
We study a generalization of the Randall-Sundrum mechanism for generating the weak/Planck hierarchy, which uses two rather than one warped extra dimension, and which requires no negative tension branes. A 4-brane with one exponentially large compact dimension plays the role of the Planck brane. We investigate the dynamical stability with respect to graviton, graviphoton and radion modes. The radion is shown to have a tachyonic instability for certain models of the 4-brane stress-energy, while it is stable in others, and massless in a special case. If stable, its mass is in the milli-eV range, …
We study the existence and stability of static kink-like configurations of a 5D scalar field, with Dirichlet boundary conditions, along the extra dimension of a warped braneworld. In the presence of gravity such configurations fail to stabilize the size of the extra dimension, leading us to consider additional scalar fields with the role of stabilization. We numerically identify multiple nontrivial solutions for a given 5D action, made possible by the nonlinear nature of the background equations, which we find is enhanced in the presence of gravity. Finally, we take a first step towards addres…
AdS3 vacua of topologically massive gravity (TMG) have been shown to be perturbatively unstable for all values of the coupling constant except the chiral point μl=1. We study the possibility that the warped vacua of TMG, which exist for all values of μ, are stable under linearized perturbations. In this paper, we show that spacelike warped AdS3 vacua with Compere-Detournay boundary conditions are indeed stable in the range μl > 3. This is precisely the range in which black hole solutions arise as discrete identifications of the warped AdS3 vacuum. The situation somewhat resembles chiral gravit…
We investigate the stability of the horizon in a warped anti-de Sitter black hole based on the three-dimensional new massive gravity by particle absorption. If a particle moving towards the black hole enters its outer horizon, the black hole changes because it absorbs conserved quantities of the particle. This variation is constrained by the equations of motion for the particle. We prove both the irreducibility of the entropy and stability of the horizon for the black hole through this process. However, the instability of the horizon is found in a near-extremal black hole by considering its se…
We demonstrate that the warped AdS3 black hole solutions of Topologically Massive Gravity are classically stable against massive scalar field perturbations by analysing the quasinormal and bound state modes of the scalar field. In particular, it is found that although classical superradiance is present it does not give rise to superradiant instabilities. The stability is shown to persist even when the black hole is enclosed by a stationary mirror with Dirichlet boundary conditions. This is a surprising result in view of the similarity between the causal structure of the warped AdS3 black hole …
This work sets up a general theoretical framework to study stability of models with a warped extra dimension where N scalar fields couple minimally to gravity. Our analysis encompasses Randall-Sundrum models with branes and bulk scalars, and general domain-wall models. We derive the Schrodinger equation governing the spin-0 spectrum of perturbations of such a system. This result is specialized to potentials generated using fake supergravity, and we show that models without branes are free of tachyonic modes. Turning to the existence of zero modes, we prove a criterion which relates the number …
New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations. To that end, the base of the warped product is assumed to be our visible 4-dimensional world, while the extra dimensions define the fibers, hence we consider "extra-dimensional evolution". Explicit conditions on the warping function that lead to geodesic incompleteness are given. These conditions can be appropriately rewritten, given a warping function, as restrictions on the intrinsic g…
We construct a quintom dark energy model with two non-minimally coupled scalar fields, one quintessence and the other phantom field, confined on the warped DGP brane. We study some important issues such as phantom divide line crossing, existence of the bouncing solutions and the stability of the solutions in this framework. We show that this model accounts for crossing of the phantom divide line and realization of the bouncing solutions. This model allows for stability of the solutions in separate regions of the $ω$-$ω'$ phase-plane.
We present a simple class of warped-product vacuum (Ricci-flat) solutions to ten and eleven-dimensional supergravity, where the internal space is flat and the warp factor supports de Sitter (dS) and anti-de Sitter (AdS) vacua in addition to trivial Minkowski vacua. We outline the construction of consistent Kaluza-Klein (KK) reductions and show that, although our vacuum solutions are non-supersymmetric, these are closely related to the bosonic part of well-known maximally supersymmetric reductions on spheres. We comment on the stability of our solutions, noting that (A)dS$_3$ vacua pass routine…
We demonstrate the relation between the Scherk-Schwarz mechanism and flipped gauged brane-bulk supergravities in five dimensions. We discuss the form of supersymmetry violating Scherk-Schwarz terms in pure supergravity and in supergravity coupled to matter. Although the Lagrangian mass terms that arise as the result of the Scherk-Schwarz redefinition of fields are naturally of the order of the inverse radius of the orbifold, the effective 4d physical mass terms are rather set by the scale \sqrt{|\barΛ|}, where \barΛ is the 4d cosmlogical constant.
The backreaction on the Randall-Sundrum warped spacetime is determined in presence of scalar field in the bulk. A general analysis shows that the stability of such a model can be achieved only if the scalar field action has non-canonical higher derivative terms. It is further shown that the gauge hierarchy problem can be resolved in such a stabilized scenario by appropriate choice of various parameters of the theory. The effective cosmological constant on the brane is shown to vanish.
We propose a simple model of extra-dimensional radius stabilization in a supersymmetric Randall-Sundrum model. In our model, we introduce only a bulk hypermultiplet and source terms (tadpole terms) on each boundary branes. With appropriate choice of model parameters, we find that the radius can be stabilized by supersymmetric vacuum conditions. Since the radion mass can be much larger than the gravitino mass and even the original supersymmetry breaking scale, radius stability is ensured even in the presence of supersymmetry breaking. We find a parameter region in which unwanted scalar masses i…
On the Stability of Warped Anti-de Sitter Spaces in Supergravity
Politecnico di Torino（都灵理工大学）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）；CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）；Texas A&M University（德克萨斯农工大学）；ENS de Lyon（里昂高等师范学校）
This work deals with the presence of twinlike models in scalar field theories. We show how to build distinct scalar field theories having the same extended solution, with the same energy density and the very same linear stability. Here, however, we start from a given but generalized scalar field theory, and we construct the corresponding twin model, which also engenders generalized dynamics. We investigate how the twinlike models arise in flat and in curved spacetime. In the curved spacetime, we consider a braneword model with the warp factor controlling the spacetime geometry with a single ex…
The stability of the modular field in a warped brane world scenario has been a subject of interest for a long time. Goldberger \& Wise ( GW ) proposed a mechanism to achieve this by invoking a massive scalar field in the bulk space-time neglecting the back-reaction. In this work, we examine the possibility of stabilizing the modulus without bringing in any external scalar field. We show that instead of flat 3-branes as considered in Randall-Sundrum ( RS ) warped braneworld model, if one considers a more generalized version of warped geometry with de-Sitter 3-brane, then the brane vacuum energy…
We consider AdS3 and warped AdS3 vacua in new massive gravity and study the highest weight modes and general propagating modes as a set of solutions for the linearized equations of motion. We observed that depending on the choice of gauge there are two types of solutions. We show that for warped AdS3 vacuum, the massless modes which appear only in the harmonic gauge have zero energy density and do not get higher curvature corrections. By computing the energy density it can be shown that all massive modes have negative energy density. Our computations prove that the massive modes in warped AdS3…
We propose a supergravity inspired derivation of a Randall-Sundrum's type action as an effective description of the dynamics of a brane coupled to the bulk through gravity only. The cosmological constants in the bulk and on the brane appear at the classical level when solving the equations of motion describing the bosonic sector of supergravities in ten and eleven dimensions coupled to the brane. They are related to physical quantities like the brane electric charge and thus inherit some of their physical properties. The most appealing property is their quantization: in d_\perp extra dimension…
We investigate stability of two branches of Freund-Rubin compactification from thermodynamic and dynamical perspectives. Freund-Rubin compactification allows not only trivial solutions but also warped solutions describing warped product of external de Sitter space and internal deformed sphere. We study dynamical stability by analyzing linear perturbations around solutions in each branch. Also we study thermodynamic stability based on de Sitter entropy. We show complete agreement of thermodynamic and dynamical stabilities of this system. Finally, we interpret the results in terms of effective e…
We review various key issues in connection with the warped braneworld models which provide us with new insights and explanations of physical phenomena through interesting geometrical features of such extra dimensional theories. Starting from the original Randall-Sundrum two brane models, we have discussed the stability, hierarchy and other important issues in connection with such braneworld. The role of higher derivative terms in the bulk for modulus stabilization has been explained. Implications of the existence of various bulk fields have been discussed and it has been shown how a warped bra…
We show that exponentially large warp factor hierarchies can be dynamically generated in supersymmetric compactifications. The compactification we consider is the supersymmetric extension of the Randall-Sundrum model. The crucial issue is the stabilization of the radius modulus for large warp factor. The stabilization sector we employ is very simple, consisting of two pure Yang--Mills sectors, one in the bulk and the other localized on a brane. The only fine-tuning required in our model is the cancellation of the cosmological constant, achieved by balancing the stabilization energy against sup…
We describe the construction of string theory models with semirealistic spectrum in a sector of (anti) D3-branes located at an orbifold singularity at the bottom of a highly warped throat geometry, which is a generalisation of the Klebanov-Strassler deformed conifold. These models realise the Randall-Sundrum proposal to naturally generate the Planck/electroweak hierarchy in a concrete string theory embedding, and yielding interesting chiral open string spectra. We describe examples with Standard Model gauge group (or left-right symmetric extensions) and three families of SM fermions, with corr…
We study a six-dimensional braneworld model with infinite warped extra dimensions in the case where the four-dimensional brane is described by a topological vortex of a U(1) symmetry-breaking Abelian Higgs model in presence of a negative cosmological constant. A detailed analysis of the microscopic parameters leading to a finite volume space-time in the extra dimensions is numerically performed. As previously shown, we find that a fine-tuning is required to avoid any kind of singularity on the brane. We then discuss the stability of the vortex by investigating the scalar part of the gauge-inva…
The `braneworld' (described by the usual worldvolume action) is a D dimensional timelike surface embedded in a N dimensional ($N>D$) warped, nonfactorisable spacetime. We first address the conditions on the warp factor required to have an extremal flat brane in a five dimensional background. Subsequently, we deal with normal deformations of such extremal branes. The ensuing Jacobi equations are analysed to obtain the stability condition. It turns out that to have a stable brane, the warp factor should have a minimum at the location of the brane in the given background spacetime. To illustrate …
The experimental value of the anomalous magnetic moment of the muon, as well as the LHCb anomalies, point towards new physics coupled non-universally to muons and electrons. Working in extra dimensional theories, which solve the electroweak hierarchy problem with a warped metric, strongly deformed with respect to the AdS$_5$ geometry at the infra-red brane, the LHCb anomalies can be solved by imposing that the bottom and the muon have a sizable amount of compositeness, while the electron is mainly elementary. Using this set-up as starting point we have proven that extra physics has to be intro…
Five-dimensional scenarios with infinitesimally thin branes replaced by appropriate configurations of a scalar field were considered. A possibility of periodic extra dimension was discussed in the presence on non-minimal scalar-gravity coupling and a generalized Gibbons-Kallosh-Linde sum rule was found. In order to avoid constraints imposed by periodicity, a non-compact spacial extra dimension was introduced. A five dimensional model with warped geometry and two thin branes mimicked by a scalar profile was constructed and discussed. In the thin brane limit the model corresponds to a set-up wit…
We investigate the thermodynamics and stability of the horizons in warped anti-de Sitter black holes of the new massive gravity under the scattering of a massive scalar field. Under scattering, conserved quantities can be transferred from the scalar field to the black hole, which change the state of the black hole. We determine that the changes in the black hole are well coincident with the laws of thermodynamics. In particular, the Hawking temperature of the black hole cannot be zero in the process as per the third law of thermodynamics. Furthermore, the black hole cannot be overspun beyond t…
In the present paper we examine, from the purely theoretical point of view and in a model-independent way, the case, when matter, gauge and Higgs fields are allowed to propagate in the bulk of five-dimensional brane world models with compact extra dimension, and the Standard Model fields and their interactions are supposed to be reproduced by the corresponding zero Kaluza-Klein modes. An unexpected result is that in order to avoid possible pathological behavior in the fermion sector, it is necessary to impose constraints on the fermion field Lagrangian. In the case when the fermion zero modes …
We investigate the stability of the extra dimensions in a warped, codimension two braneworld that is based upon an Einstein-Maxwell-dilaton theory with a non-vanishing scalar field potential. The braneworld solution has two 3-branes, which are located at the positions of the conical singularities. For this type of brane solution the relative positions of the branes (the shape modulus) is determined via the tension-deficit relations, if the brane tensions are fixed. However, the volume of the extra dimensions (the volume modulus) is not fixed in the context of the classical theory, implying we …
We discuss the spectrum of the tensor metric perturbations and the stability of warped compactifications with the de Sitter spacetime in the higher-dimensional gravity. The spacetime structure is given in terms of the warped product of the non-compact direction, the spherical internal dimensions and the four-dimensional de Sitter spacetime. To realize a finite bulk volume, we construct the brane world model, using the cut-copy-paste method. Then, we compactify the spherical directions on the brane. In any case, we show the existence of the massless zero mode and the mass gap of it with massive…
Stability and causality are investigated for quantum field theories incorporating Lorentz and CPT violation. Explicit calculations in the quadratic sector of a general renormalizable lagrangian for a massive fermion reveal that no difficulty arises for low energies if the parameters controlling the breaking are small, but for high energies either energy positivity or microcausality is violated in some observer frame. However, this can be avoided if the lagrangian is the sub-Planck limit of a nonlocal theory with spontaneous Lorentz and CPT violation. Our analysis supports the stability and cau…
A simple model of extra-dimensional radius stabilization in a supersymmetric Randall-Sundrum model is presented. In our model, we introduce only a bulk hypermultiplet and source terms on each boundary branes. With an appropriate choice of model parameters, we find that the radius can be stabilized by supersymmetric vacuum conditions. Since the radion mass can be much larger than the gravitino mass and the supersymmetry breaking scale, the radius stability is ensured even with the supersymmetry breaking. We find a parameter region where unwanted scalar masses induced by quantum corrections thro…
In the present work we investigate the existence and stability properties of q-balls which consist of a couple of scalar fields, forming an SU(2) doublet in a Lagrangian with a global SU(2) symmetry. We find that these spinors can form a localized and stable field configuration, if they rotate in their internal SU(2) space. We find the energy and charge of the soliton in both thin and thick-wall approximation and we prove its stability against decaying to free particles. We also find the asymptotic forms of the scalar and gauge field and the energy and charge of the configuration when the SU(2…
In the paradigm with a small warped Spacelike Extra Dimensions (SED), the Higgs field is in general localized at a boundary of the SED (TeV-brane) where the gravity scale is redshifted to the TeV by a warp factor. If the SM gauge bosons and fermions propagate into the warped SED, one can generate the mass hierarchy for fermions. It is thus crucial to treat carefully the TeV-brane localized masses for such fermions, which is done in the literature by applying a regularization process suffering from a lack of consistency and more importantly being useless, as we demonstrate in detail in the pres…
The quantization of a vector model presenting spontaneous breaking of Lorentz symmetry in flat Minkowski spacetime is discussed. The Stueckelberg trick of introducing an auxiliary field along with a local symmetry in the initial Lagrangian is used to convert the second-class constraints present in the initial Lagrangian to first-class ones. An additional deformation is employed in the resulting Lagrangian to handle properly the first-class constraints, and the equivalence with the initial model is demonstrated using the BRST invariance of the deformed Lagrangian. The framework for performing p…
We investigate the dynamical stability of warped, axially symmetric compactifications in anomaly free 6D gauged supergravity. The solutions have conical defects, which we source by 3-branes placed on orbifold fixed points, and a smooth limit to the classic sphere-monopole compactification. Like for the sphere, the extra fields that are generically required by anomaly freedom are especially relevant for stability. With positive tension branes only, there is a strict stability criterion (identical to the sphere case) on the charges present under the monopole background. Thus brane world models w…
We initiate a comprehensive study of a set of solutions of topologically massive gravity known as null warped anti-de Sitter spacetimes. These are pp-wave extensions of three-dimensional anti-de Sitter space. We first perform a careful analysis of the linearized stability of black holes in these spacetimes. We find two qualitatively different types of solutions to the linearized equations of motion: the first set has an exponential time dependence, the second - a polynomial time dependence. The solutions polynomial in time induce severe pathologies and moreover survive at the non-linear level.…
We study the perturbative stability of magnetic black holes in a general class of nonlinear electrodynamics, where the Lagrangian is given by a general function of the field strength of electromagnetic field $F_{μν}$ and its Hodge dual $\widetilde{F}_{μν}$. We derive sufficient conditions for the stability of the black holes. We apply the stability conditions to Bardeen's regular black holes, black holes in Euler-Heisenberg theory, and black holes in Born-Infeld theory. As a result, we obtain a sufficient condition for the stability of Bardeen's black holes, which restricts $F_{μν}\widetilde{F…
For classical relativistic field theory in Minkowski space-time, the addition of a superpotential term to a conserved current density is trivial in the sense that it does not modify the local conservation law nor change the conserved charge, though it may allow us to obtain a current density with some improved properties. The addition of a total derivative term to a Lagrangian density is also trivial in the sense that it does not modify the equations of motion of the theory. These facts suggest that both operations are related and possibly equivalent to each other for any global symmetry of an…
Guided by the symmetries of the Euler-Lagrange equations of motion, a study of the constrained dynamics of singular Lagrangians is presented. We find that these equations of motion admit a generalized Lie symmetry, and on the Lagrangian phase space the generators of this symmetry lie in the kernel of the Lagrangian two-form. Solutions of the energy equation\textemdash called second-order, Euler-Lagrange vector fields (SOELVFs)\textemdash with integral flows that have this symmetry are determined. Importantly, while second-order, Lagrangian vector fields are not such a solution, it is always po…
