The Randall-Sundrum model is studied in 6 dimension with AdS$_4$ or dS$_4$ metric in the physical 4 dimensional space. Two solutions are found, one with induced 5-dimensional gravity terms added to the induced cosmological constant terms. We study the graviton modes in both solutions by transforming the mass eigenvalue equation to a Schrodinger equation with a volcano potential. The spectrum of gravitational excitations depends on the input parameters of the theory, the six dimensional and the effective four-dimensional cosmological constants. The model gives a physically acceptable spectrum if the 4 dimensional cosmological constant is sufficiently small.
Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3 dimensional self-dual space-like warped $AdS_3$ black hole background. We argue that in this background, symmetric conditions and gauge constraint can not be satisfied simultaneously. Using new suitable constraint, we find the exact solutions of equation of motion. Then, we obtain the quasi-normal modes by imposing appropriate boundary condition at horizon and infinity.
We investigate stationary, rotationally symmetric solutions of a recently proposed three-dimensional theory of massive gravity. Along with BTZ black holes, we also obtain warped AdS_3 black holes, and (for a critical value of the cosmological constant) AdS_2 x S^1 as solutions. The entropy, mass and angular momentum of these black holes are computed.
We consider null warped AdS(3) solutions of three-dimensional gravity coupled to a massive vector field. We isolate a certain set of non-propagating solutions to the equations of motion, which we argue are the ones relevant for understanding the stress tensor sector of the dual field theory. We construct a map from these modes to solutions of three-dimensional Einstein gravity with a negative cosmological constant, and thus show that they admit a Fefferman-Graham-like asymptotic expansion. We also compute the renormalized on-shell action for these modes at full non-linear level and propose tha…
As a follow-up to our previous paper arxiv: 1309.4244[hep-th], we determine radion induced spherically symmetric solution using the gradient approximation scheme, when two warped $3$-branes are slant with respect to each other such that the radion field in this case is a radial co-ordinate varying function. The slanting between the branes is assumed to be small. In the absence of any on-brane matter except that induced effects of radion field, the resulting black hole is found to be extremal Reissner-Nordstrom whose mass is proportional to the slanting between the $3$-branes. It is however see…
We discuss physical implications of the four-dimensional effective supergravity, that describes low-energy physics of the Randall--Sundrum model with moduli fields in the bulk and charged chiral matter living on the branes. Cosmological constant can be cancelled through the introduction of a brane Polonyi field and a brane superpotential for the 4d dilaton. We deduce a generalization of the effective 4d action to the case of a general, not necessarily exponential, warp factor. We note, that breakdown of supersymmetry in generic warped models may lead to the stabilization of the interbrane dist…
We formulate several criteria under which the symmetries associated with the Killing and Killing-Yano tensors on the base space can be lifted to the symmetries of the full warped geometry. The procedure is explicitly illustrated on several examples, providing new prototypes of spacetimes admitting such tensors. In particular, we study a warped product of two Kerr-NUT-(A)dS spacetimes and show that it gives rise to a new class of highly symmetric vacuum (with cosmological constant) black hole solutions that inherit many of the properties of the Kerr-NUT-(A)dS geometry.
We investigate the discretized version of the compact Randall-Sundrum model. By studying the mass eigenstates of the lattice theory, we demonstrate that for warped space, unlike for flat space, the strong coupling scale does not depend on the IR scale and lattice size. However, strong coupling does prevent us from taking the continuum limit of the lattice theory. Nonetheless, the lattice theory works in the manifestly holographic regime and successfully reproduces the most significant features of the warped theory. It is even in some respects better than the KK theory, which must be carefully …
We classify all stationary axi-symmetric solutions of topologically massive gravity into Einstein, Schrödinger, warped and generic solutions. We construct explicitly all local solutions in the first three sectors and present an algorithm for the numerical construction of all local solutions in the generic sector. The only input for this algorithm is the value of one constant of motion if the solution has an analytic centre, and three constants of motion otherwise. We present several examples, including soliton solutions that asymptote to warped AdS.
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.
We present a cosmic string on a warped five dimensional space time in Einstein-Yang-Mills theory. Four-dimensional cosmic strings show some serious problems concerning the mechanism of string smoothing related to the string mass per unit length, $Gμ\approx 10^{-6}$. A warped cosmic string could overcome this problem and also the superstring requirement that $Gμ$ must be of order 1, which is far above observational bounds. Also the absence of observational evidence of axially symmetric lensing effect caused by cosmic strings could be explained by the warped cosmic string model we present: the a…
We investigate five dimensional Einstein spaces in warped geometries from the point of view of the four dimensional physically relevant Robertson-Walker-Friedman cosmological metric and the Schwarzschild metric. We show that a four-dimensional cosmology with a closed spacelike section and a cosmological constant can be imbedded into five-dimensional flat space-time.
The version of the warp model that we proposed to explain the mass scale hierarchy has been extended by the introduction of one or more singularities in the metric. We restricted ourselves to a real massless scalar field supposed to propagate in a five dimensional bulk with the extradimension being compactified on a strip or on a circle. With the same emphasis on the hermiticity and commutativity properties of the Kakuza Klein operators, we have established all the allowed boundary conditions to be imposed on the fields. From them, for given positions of the singularities, one can deduce eithe…
Motivated by the construction of holographic duals to five-dimensional superconformal quantum field theories, we obtain global solutions to Type IIB supergravity invariant under the superalgebra $F(4)$ on a space-time of the form $AdS_6 \times S^2$ warped over a two-dimensional Riemann surface $Σ$. In earlier work, the general local solutions were expressed in terms of two locally holomorphic functions $\mathcal A_\pm$ on $Σ$ and global solutions were sketched when $Σ$ is a disk. In the present paper, the physical regularity conditions on the supergravity fields required for global solutions a…
We give a direct computation of the mass of black holes in Warped Anti-de Sitter space (WAdS) in terms of the Brown-York stress-tensor at the boundary. This permits to explore to what extent the holographic renormalization techniques can be applied to such type of deformation of AdS. We show that, despite some components of the boundary stress-tensor diverge and resist to be regularized by the introduction of local counterterms, the precise combination that gives the quasilocal energy density yields a finite integral. The result turns out to be in agreement with previous computations of the bl…
Supersymmetry breaking and radius stabilization by constant superpotentials localized at boundaries is studied in a supersymmetric warped space model where a hypermultiplet, a compensator and a radion multiplet are taken into account. Soft mass induced by the anomaly mediation can be of the order of 100GeV and can be dominant compared to that mediated by bulk fields. A lighter physical mode composed of the radion and the moduli can have mass of the order of a TeV and the gravitino mass can be of the order of 10^7 GeV. The radius is stabilized by the presence of the constant boundary superpoten…
We find a cosmological solution corresponding to compactification of 10d supergravity on a warped conifold that easily circumvents `no-go' theorem given for a warped/flux compactification, providing new perspectives for the study of supergravity or superstring theory in cosmological backgrounds. With fixed volume moduli of the internal space, the model can explain a physical universe undergoing an accelerated expansion in the 4d Einstein frame, for a sufficiently long time. The solution found in the limit that the warp factor dependent on the radial coordinate $y$ is extremized (giving a const…
We present the "classical" Nielsen-Olesen vortex solution on a warped five dimensional space time, where we solved the effective four-dimensional equations from the five-dimensional equations together with the junction and boundary conditions. Four dimensional cosmic strings show some serious problems concerning the mechanism of string smoothing related to the string mass per unit length, $Gμ\leq 10^{-6}$. Moreover, there is no observational evidence of axially symmetric lensing effect caused by cosmic strings. Also super-massive cosmic strings ($Gμ\gtrsim 1$), predicted by superstring theory,…
We present the 5-dimensional cosmological solutions in the Randall-Sundrum warped compactification scenario, using the Goldberger-Wise mechanism to stabilize the size of the extra dimension. Matter on the Planck and TeV branes is treated perturbatively, to first order. The back-reaction of the scalar field on the metric is taken into account. We identify the appropriate gauge-invariant degrees of freedom, and show that the perturbations in the bulk scalar can be gauged away. We confirm previous, less exact computations of the shift in the radius of the extra dimension induced by matter. We poi…
We explore in detail the prospects of obtaining a four-dimensional de Sitter universe in classical supergravity models with warped and time-independent extra dimensions, presenting explicit cosmological solutions of the $(4+n)$-dimensional Einstein equations with and without a bulk cosmological constant term. For the first time in the literature we show that there may exist a large class of warped supergravity models with a noncompact extra dimension which lead to a finite 4D Newton constant as well as a massless 4D graviton localised on an inflating four-dimensional FLRW universe. This result…
We report on explicit cosmological solutions within the framework of an inflating de Sitter brane embedded in five- and ten-dimensional bulk spacetimes. In the specific example we study the brane tension is induced by the curvature related to the expansion of a physical 3+1 spacetime rather than by a bulk cosmological term. In a generic situation with nonzero brane tension, the expansion of the universe accelerates eventually. We also show that inflationary cosmology is possible for a wide class of metrics without violating four- and higher-dimensional null energy condition.
A warped space model with a constant boundary superpotential has been an efficient model both to break supersymmetry and to stabilize the radius, when hypermultiplet, compensator and radion multiplet are taken into account. In such a model of the radius stabilization, the radion and moduli masses, the gravitino mass and the induced soft masses are studied. We find that a lighter physical mode composed of the radion and the moduli can have mass of the order of a TeV and that the gravitino mass can be of the order of 10$^7$ GeV. It is also shown that soft mass induced by the anomaly mediation ca…
We study deconstructed gauge theories in which a warp factor emerges dynamically and naturally. We present nonsupersymmetric models in which the potential for the link fields has translational invariance, broken only by boundary effects that trigger an exponential profile of vacuum expectation values. The spectrum of physical states deviates exponentially from that of the continuum for large masses; we discuss the effects of such exponential towers on gauge coupling unification. We also present a supersymmetric example in which a warp factor is driven by Fayet-Iliopoulos terms. The model is pe…
We develop a perturbative expansion scheme for solving general boundary value problems in a broad class of type IIB flux compactifications. The background solution is any conformally Calabi-Yau compactification with imaginary self-dual (ISD) fluxes. Upon expanding in small deviations from the ISD solution, the equations of motion simplify dramatically: we find a simple basis in which the n-th order equations take a triangular form. This structure implies that the system can be solved iteratively whenever the individual, uncoupled equations can be solved. We go on to demonstrate the solution of…
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…
The characterization of a six- (or seven)-dimensional internal manifold with metric as having positive, zero or negative curvature is expected to be an important aspect of warped compactifications in supergravity. In this context, Douglas and Kallosh recently pointed out that a compact internal space with negative curvature could help to construct four-dimensional de Sitter solutions only if the extra dimensions are strongly warped or there are large stringy corrections. That is, the problem of finding 4-dimensional de Sitter solutions is well posed, if all extra dimensions are physically comp…
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…
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.…
The structure of state vector space for a general (non-anomalous) gauge theory is studied within the Lagrangian version of the $Sp(2)$-symmetric quantization method. The physical {\it S}-matrix unitarity conditions are formulated. The general results are illustrated on the basis of simple gauge theory models.
We analyze supersymmetric solutions of M-theory based an a seven-dimensional internal space with SU(3) structure and a four-dimensional maximally symmetric space. The most general supersymmetry conditions are derived and we show that a non-vanishing cosmological constant requires the norms of the two internal spinors to differ. We find explicit local solutions with singlet flux and the space being a warped product of a circle, a nearly-Kahler manifold and AdS_4. The embedding of solutions into heterotic M-theory is also discussed.
We study a supersymmetry breaking deformation of the M-theory background found in arXiv:hep-th/0012011. The supersymmetric solution is a warped product of R^{2,1} and the 8-dimensional Stenzel space, which is a higher dimensional generalization of the deformed conifold. At the bottom of the warped throat there is a 4-sphere threaded by \tilde{M} units of 4-form flux. The dual (2+1)-dimensional theory has a discrete spectrum of bound states. We add p anti-M2 branes at a point on the 4-sphere, and show that they blow up into an M5-brane wrapping a 3-sphere at a fixed azimuthal angle on the 4-sph…
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 …
In this paper we apply the anholonomic frames method developed in refs. [1-4] to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off--diagonal 5D metric, parameterized in terms of several ansatz functions, we show that using anholonomic frames greatly simplifies the resulting Einstein field equations. These simplified equations contain an interesting freedom in that one can chose one of the ansatz functions and then determine the remaining ansatz functions in terms of this choice. As examples we take one of the ansatz functions to be a solitonic solu…
We take arbitrary gravitational perturbations of a 5d spacetime and reduce it to the form an axially symmetric warped braneworld. Then, we write the filed equations for the linearized gravity perturbations. We obtain the equations that describes the graviton, gravivector and the graviscalar fluctuations and analyse the effects of the Schrödinger potentials that appear in these equations.
Generic cosmological models derived from higher dimensional theories with warped extra dimensions have a nonzero cosmological constant-like term induced on the 3+1 space-time, or a physical 3-brane. In the scenario where this 3+1 space-time is an inflating de Sitter "brane" embedded in a higher-dimensional space-time, described by warped geometry, the 4D cosmological term is determined in terms of two length scales: one is a scale associated with the size of extra dimension(s) and the other is a scale associated with the warping of extra space(s). The existence of this term in four dimensions …
We study a 5d gravity theory with a warped metric and show that two N = 2 supersymmetric quantum-mechanical systems are hidden in the 4d spectrum. The supersymmetry can be regarded as a remnant of higher-dimensional general coordinate invariance and turns out to become a powerful tool to determine the physical 4d spectrum and the allowed boundary conditions. Possible extensions of the N = 2 supersymmetry are briefly discussed.
