Warped Spacetime Research Articles

Supersymmetry with light stops

Recent LHC data, together with the electroweak naturalness argument, suggest that the top squarks may be significantly lighter than the other sfermions. We present supersymmetric models in which such a split spectrum is obtained through "geometries": being "close to" electroweak symmetry breaking implies being "away from" supersymmetry breaking, and vice versa. In particular, we present models in 5D warped spacetime, in which supersymmetry breaking and Higgs fields are located on the ultraviolet and infrared branes, respectively, and the top multiplets are localized to the infrared brane. The hierarchy of the Yukawa matrices can be obtained while keeping near flavor degeneracy between the first two generation sfermions, avoiding stringent constraints from flavor and CP violation. Through the AdS/CFT correspondence, the models can be interpreted as purely 4D theories in which the top and Higgs multiplets are composites of some strongly interacting sector exhibiting nontrivial dynamics at a low energy. Because of the compositeness of the Higgs and top multiplets, Landau pole constraints for the Higgs and top couplings apply only up to the dynamical scale, allowing for a relatively heavy Higgs boson, including m_h = 125 GeV as suggested by the recent LHC data. We analyze electroweak symmetry breaking for a well-motivated subset of these models, and find that fine-tuning in electroweak symmetry breaking is indeed ameliorated. We also discuss a flat space realization of the scenario in which supersymmetry is broken by boundary conditions, with the top multiplets localized to a brane while other matter multiplets delocalized in the bulk.

Towards non-AdS holography in 3-dimensional higher spin gravity

We take the first steps towards non-AdS holography in higher spin gravity. Namely, we propose a variational principle for generic 3-dimensional higher spin gravity that accommodates asymptotic backgrounds beyond AdS, like asymptotically Schrodinger, Lifshitz or warped AdS spacetimes. As examples we study in some detail the four sl(2) embeddings of spin-4 gravity and provide associated geometries, including an asymptotic Lifshitz black hole.

Hidden-sector current-current correlators in holographic gauge mediation

We discuss gauge mediation in the case where the hidden sector is strongly coupled but, via the gauge-gravity correspondence, admits a weakly-coupled description in terms of a warped higher-dimensional spacetime. In this framework, known as holographic gauge mediation, the visible-sector gauge group is realized in the gravitational description by probe D-branes and the nonsupersymmetric state by normalizable perturbations to the geometry. Using the formalism of general gauge mediation, supersymmetry-breaking soft terms in the visible sector can be related to the two-point functions of the hidden-sector current superfield that couples to the visible-sector gauge group. Such correlation functions cannot be directly calculated in the strongly coupled field theory but can be determined using the gauge-gravity correspondence and holographic renormalization. We explore this procedure by considering a toy geometry where such two-point functions can be explicitly calculated. Unlike previous implementations of holographic gauge mediation where sfermion masses were not calculable directly in a purely holographic framework, such terms are readily obtained via these correlators, while (due to the simplicity of the geometry considered) the visible-sector gauginos remain massless to leading order in the visible-sector coupling.

Observing signals of the bulk matter Randall-Sundrum model through rare decays of supersymmetric particles

The bulk matter Randall-Sundrum (RS) model is a setup where standard model (SM) matter and gauge fields reside in the bulk of 5D warped spacetime while the Higgs field is confined on the IR brane. The wave functions of the 1st and 2nd generation matter particles are localized toward the UV brane and those of the 3rd generation toward the IR brane, so that the hierarchical structure of the Yukawa couplings arises geometrically without hierarchy in fundamental parameters. This paper discusses observing signals of this model in the case where the Kaluza-Klein scale is far above the collider scale, but the model is combined with the 5D minimal supersymmetric standard model (MSSM) and supersymmetric (SUSY) particles are in the reach of collider experiments. A general SUSY breaking mass spectrum consistent with the bulk matter RS model is considered: a SUSY breaking sector locates on the IR brane and its effects are mediated to 5D MSSM through a hybrid of gravity mediation, gaugino mediation, and gauge mediation. This paper argues that it is possible to observe the signals of the bulk matter RS model through rare decays of ``almost SU(2) singlet mass eigenstates'' that are induced by flavor-violating gravity mediation contributions to matter soft SUSY breaking terms.

Asymptotically warped anti-de Sitter spacetimes in topologically massive gravity

Asymptotically warped AdS spacetimes in topologically massive gravity with negative cosmological constant are considered in the case of spacelike stretched warping, where black holes have been shown to exist. We provide a set of asymptotic conditions that accommodate solutions in which the local degree of freedom (the "massive graviton") is switched on. An exact solution with this property is explicitly exhibited and possesses a slower fall-off than the warped AdS black hole. The boundary conditions are invariant under the semidirect product of the Virasoro algebra with a u(1) current algebra. We show that the canonical generators are integrable and finite. When the graviton is not excited, our analysis is compared and contrasted with earlier results obtained through the covariant approach to conserved charges. In particular, we find agreement with the conserved charges of the warped AdS black holes as well as with the central charges in the algebra.

Detailed study of null and timelike geodesics in the Alcubierre warp spacetime

The Alcubierre warp spacetime yields a fascinating chance for comfortable interstellar travel between arbitrary distant places without the time dilation effect as in special relativistic flights. Even though the warp spacetime needs exotic matter for its construction and is thus far from being physically feasible, it offers a rich playground for studying geodesics in the general theory of relativity. This paper is addressed to graduate students who have finished a first course in general relativity to give them a deeper inside in the calculation of non-affinely parametrized null and time-like geodesics and a straightforward approach to determine the gravitational lensing effect due to curved spacetime by means of the Jacobi equation. Both topics are necessary for a thorough discussion of the visual effects as observed by a traveller inside the warp bubble or a person looking from outside. The visual effects of the traveller can be reproduced with an interactive Java application.

High-energy photon-hadron scattering in holographic QCD

This article provides an in-depth look at hadron high-energy scattering by using gravity dual descriptions of strongly coupled gauge theories. Just like deeply inelastic scattering (DIS) and deeply virtual Compton scattering (DVCS) serve as clean experimental probes into nonperturbative internal structure of hadrons, elastic scattering amplitude of a hadron and a (virtual) photon in gravity dual can be exploited as a theoretical probe. Since the scattering amplitude at sufficiently high energy (small Bjorken $x$) is dominated by parton contributions ($=\mathrm{\text{Pomeron contributions}}$) even in strong coupling regime, there is a chance to learn a lesson for generalized parton distribution (GPD) by using gravity dual models. We begin with refining derivation of the Brower--Polchinski--Strassler--Tan (BPST) Pomeron kernel in gravity dual, paying particular attention to the role played by the complex spin variable $j$. The BPST Pomeron on warped spacetime consists of a Kaluza--Klein tower of 4D Pomerons with nonlinear trajectories, and we clarify the relation between Pomeron couplings and the Pomeron form factor. We emphasize that the saddle-point value ${j}^{*}$ of the scattering amplitude in the complex $j$-plane representation is a very important concept in understanding qualitative behavior of the scattering amplitude. The total Pomeron contribution to the scattering is decomposed into the saddle-point contribution and at most a finite number of pole contributions, and when the pole contributions are absent (which we call saddle-point phase), kinematical variable $(q,x,t)$-dependence of $\mathrm{ln}(1/q)$ evolution and $\mathrm{ln}(1/x)$ evolution parameters ${\ensuremath{\gamma}}_{\mathrm{eff}}$ and ${\ensuremath{\lambda}}_{\mathrm{eff}}$ in DIS and $t$-slope parameter $B$ of DVCS in HERA experiment are all reproduced qualitatively in gravity dual. All of these observations shed a new light on modeling of GPD. Straightforward application of those results to other hadron high-energy scattering is also discussed.

New examples of marginally trapped surfaces and tubes in warped spacetimes

By using the classical Hopf map, we construct another fibration that allows us to obtain examples of marginally trapped tori and marginally outer trapped tubes (MOTT) which are foliated by tori, all of them embedded in a closed Friedman-Lemaître-Robertson-Walker 4-spacetime. In addition, we show examples of MOTTs with any causal character.

Five-Dimensional Warped Product Space-Time with Time-Dependent Warp Factor and Cosmology of the Four-Dimensional Universe

In this paper, we have studied a 5-dimensional warped product space-time with a time-dependent warp factor. This warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe and leads to a geometric interpretation of dynamical dark energy. The five-dimensional field equations are constructed and its solutions are obtained. The nature of modifications produced by this warp factor in the bulk geometry is discussed. The hypersurface is described by a flat FRW-type metric in the ordinary spatial dimension. It is found that the effective cosmological constant of the four-dimensional universe is a variable quantity monitored by the time-dependent warp factor. The universe is initially decelerated, but subsequently makes a transition to an accelerated phase at later times.

Effects of temperature on thick branes and the fermion (quasi-)localization

Following Campos's work [Phys. Rev. Lett. 88, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Following Campos's work [Phys. Rev. Lett. \textbf{88}, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Sitter (AdS) thick branes in five-dimensional (5D) warped spacetime, and on the fermion (quasi-)localization. First, in the case of flat brane, when the critical temperature reaches, the solution of the background scalar field and the warp factor is not unique. So the thickness of the flat thick brane is uncertain at the critical value of the temperature parameter, which is found to be lower than the one in flat 5D spacetime. The mass spectra of the fermion Kaluza-Klein (KK) modes are continuous, and there is a series of fermion resonances. The number and lifetime of the resonances are finite and increase with the temperature parameter, but the mass of the resonances decreases with the temperature parameter. Second, in the case of dS brane, we do not find such a critical value of the temperature parameter. The mass spectra of the fermion KK modes are also continuous, and there is a series of fermion resonances. The effects of temperature on resonance number, lifetime, and mass are the same with the case of flat brane. Last, in the case of AdS brane, {the critical value of the temperature parameter can less or greater than the one in the flat 5D spacetime.} The spectra of fermion KK modes are discrete, and the mass of fermion KK modes does not decrease monotonically with increasing temperature parameter.

On higher order geometric and renormalization group flows

Renormalization group (RG) flows of the bosonic nonlinear σ -model are governed, perturbatively, at different orders of α ′ , by perturbatively evaluated β -functions. In regions where α ′ R c 2 ≪ 1 ( 1 R c 2 represents the curvature scale), the flow equations at various orders in α ′ can be thought of as approximating the full, non-perturbative RG flow. On the other hand, taking a different viewpoint, we may consider the above-mentioned RG flow equations as viable geometric flows in their own right, without any reference to the RG aspect. Looked at as purely geometric flows where higher order terms appear, we no longer have the perturbative restrictions (small curvatures). In this paper, we perform our analysis from both these perspectives using specific target manifolds such as S 2 , H 2 , unwarped S 2 × H 2 and simple warped products. We analyse and solve the higher order RG flow equations within the appropriate perturbative domains and find the corrections arising due to the inclusion of higher order terms. Such corrections, within the perturbative regime, are shown to be small and they provide an estimate of the error that arises when higher orders are ignored. We also investigate higher order geometric flows on the same manifolds and figure out generic features of geometric evolution, the appearance of singularities and solitons. The aim, in this context, is to demonstrate the role of higher order terms in modifying the flow. One interesting aspect of our analysis is that, separable solutions of the higher order flow equations for simple warped spacetimes (of the kind used in bulk-brane models with a single extra dimension), correspond to constant curvature anti de Sitter (AdS) spacetimes, modulo an overall flow parameter dependent scale factor. The functional form of this scale factor (that we obtain) changes on the inclusion of successive higher order terms in the flow.

On higher dimensional Einstein spacetimes with a warped extra dimension

We study a class of higher dimensional warped Einstein spacetimes with one extra dimension. These were originally identified by Brinkmann as those Einstein spacetimes that can be mapped conformally on other Einstein spacetimes, and have subsequently appeared in various contexts to describe, e.g., different braneworld models or warped black strings. After clarifying the relation between the general Brinkmann metric and other more specific coordinate systems, we analyze the algebraic type of the Weyl tensor of the solutions. In particular, we describe the relation between Weyl aligned null directions of the lower dimensional Einstein slices and of the full spacetime, which in some cases can be algebraically more special. Possible spacetime singularities introduced by the warp factor are determined via a study of scalar curvature invariants and Weyl components measured by geodetic observers. Finally, we illustrate how Brinkmann's metric can be employed to generate new solutions by presenting the metric of spinning and accelerating black strings in five-dimensional anti-de Sitter space.

Geodesic congruences in warped spacetimes

In this article, we explore the kinematics of timelike geodesic congruences in warped five dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall--Sundrum AdS (Anti de Sitter) geometry without and with branes we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer's point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

GAUGE-HIGGS UNIFICATION: STABLE HIGGS BOSONS AS COLD DARK MATTER

In the gauge-Higgs unification the 4D Higgs field becomes a part of the extra-dimensional component of the gauge potentials. In the SO(5) × U(1) gauge-Higgs unification in the Randall-Sundrum warped spacetime the electroweak symmetry is dynamically broken through the Hosotani mechanism. The Higgs bosons become absolutely stable, and become the dark matter of the universe. The mass of the Higgs boson is determined from the WMAP data to be about 70 GeV.

The curious case of null warped space

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. In order to make sense of these geometries, it is thus crucial to impose appropriate boundary conditions. We argue that there exists a consistent set of boundary conditions that allows us to reject the above pathological modes from the physical spectrum. The asymptotic symmetry group associated to these boundary conditions consists of a centrally-extended Virasoro algebra. Using this central charge we can account for the entropy of the black holes via Cardy’s formula. Finally, we note that the black hole spectrum is chiral and prove a Birkoff theorem showing that there are no other stationary axisymmetric black holes with the specified asymptotics. We extend most of the analysis to a larger family of pp-wave black holes which are related to Schrödinger spacetimes with critical exponent z.

Effects of the variation of mass on fermion localization and resonances on thick branes

A few years ago, Campos investigated the critical phenomena of thick branes in warped spacetimes [Phys. Rev. Lett. 88, 141602 (2002)]. Inspired by his work, we consider a toy model of thick branes generated by a real scalar field with the potential $V(\ensuremath{\phi})=a{\ensuremath{\phi}}^{2}\ensuremath{-}b{\ensuremath{\phi}}^{4}+c{\ensuremath{\phi}}^{6}$, and investigate the variation of the mass parameter $a$ on the branes as well as the localization and resonances of fermions. An interesting result is found: there is a critical value for the mass parameter $a$, and when the critical value of $a$ is reached the solution of the background scalar field is not unique and has the shape of a double kink. This happens in both cases with and without gravity. It is also shown that the numbers of the bound Kaluza-Klein modes of fermions on the gravity-free brane and the resonant states of fermions on the brane with gravity increase with the value of $a$.

An intrinsic characterization of 2 + 2 warped spacetimes

We give several equivalent conditions that characterize the 2 + 2 warped spacetimes: imposing the existence of a Killing–Yano tensor A subject to complementary algebraic restrictions, in terms of the projector v (or of the canonical 2-form U) associated with the 2-planes of the warped product. These planes are the principal planes of the Weyl and/or Ricci tensors and can be explicitly obtained from them. Therefore, we obtain the necessary and sufficient (local) conditions for a metric tensor to be a 2 + 2 warped product. These conditions exclusively involve explicit concomitants of the Riemann tensor. We present a similar analysis for the conformally 2 + 2 product spacetimes and give an invariant classification of them. The warped products correspond to two of these invariant classes. The more degenerate class is the set of product metrics which are also studied from an invariant point of view. The interest of these results in labeling specific solutions of the Einstein equations is outlined.

RICCI FLOW OF UNWARPED AND WARPED PRODUCT MANIFOLDS

We analyze Ricci flow (normalized/unnormalized) of product manifolds — unwarped as well as warped, through a study of generic examples. First, we investigate such flows for the unwarped scenario with manifolds of the type 𝕊n × 𝕊m, 𝕊n × ℍm, ℍm × ℍn and also, similar multiple products. We are able to single out generic features such as singularity formation, isotropization at particular values of the flow parameter and evolution characteristics. Subsequently, motivated by warped braneworlds and extra dimensions, we look at Ricci flows of warped space–times. Here, we are able to find analytic solutions for a special case by variable separation. For others, we numerically solve the equations and draw certain useful inferences about the evolution of the warp factor, the scalar curvature as well as the occurrence of singularities at finite values of the flow parameter. We also investigate the dependence of the singularities of the flow on the initial conditions. We expect our results to be useful in any physical/mathematical context where such product manifolds may arise.

Confinement of test particles in warped spacetimes

We investigate test particle trajectories in warped spacetimes with a thick brane warp factor, a cosmological on-brane line element, and a time dependent extra dimension. The geodesic equations are reduced to a first order autonomous dynamical system. Using analytical methods, we arrive at some useful general conclusions regarding possible trajectories. Oscillatory motion, suggesting confinement about the location of the thick brane, arises for a growing warp factor. On the other hand, we find runaway trajectories (exponential-like) for a decaying warp factor. Variations of the extra dimensional scale factor yield certain quantitative differences. Results obtained from explicit numerical evaluations match well with the qualitative conclusions obtained from the dynamical systems analysis.

Geometric finiteness, holography and quasinormal modes for the warped AdS3 black hole

We show that there exists a precise kinematical notion of holography for the Euclidean warped AdS3 black hole. This follows from the fact that the Euclidean warped AdS3 black hole spacetime is a geometrically finite hyperbolic manifold. For such manifolds a theorem of Sullivan provides a one-to-one correspondence between the hyperbolic structure in the bulk and the conformal structure of its boundary. Using this theorem we obtain the holographic quasinormal modes for the warped AdS3 black hole.