Six-dimensional Bulk Research Articles

Lukewarm black holes in the Nash-Greene framework

In this work, we investigate the embedding of a four-dimensional spherically symmetric metric in a six-dimensional bulk. By using the Nash-Greene embedding theorem, the additional $SO(2)$ symmetry of the two spacelike extra dimensions induces the appearance of horizons of a lukewarm charged black hole. In addition, a mass-dependent cosmological constant is obtained with a prediction of a bound for the mass and minimal charge.

Towards a gravity dual for the large scale structure of the universe

The dynamics of the large-scale structure of the universe enjoys at all scales, even in the highly non-linear regime, a Lifshitz symmetry during the matter-dominated period. In this paper we propose a general class of six-dimensional spacetimes which could be a gravity dual to the four-dimensional large-scale structure of the universe. In this set-up, the Lifshitz symmetry manifests itself as an isometry in the bulk and our universe is a four-dimensional brane moving in such six-dimensional bulk. After finding the correspondence between the bulk and the brane dynamical Lifshitz exponents, we find the intriguing result that the preferred value of the dynamical Lifshitz exponent of our observed universe, at both linear and non-linear scales, corresponds to a fixed point of the RGE flow of the dynamical Lifshitz exponent in the dual system where the symmetry is enhanced to the Schrodinger group containing a non-relativistic conformal symmetry. We also investigate the RGE flow between fixed points of the Lifshitz dynamical exponent in the bulk and observe that this flow is reflected in a growth rate of the large-scale structure, which seems to be in qualitative agreement with what is observed in current data. Our set-up might provide an interesting new arena for testing the ideas of holography and gravitational duals.

Bulk gauge and matter fields in nested warping: II. Symmetry breaking and phenomenological consequences

Generalizing the Randall-Sundrum scenario to higher dimensions with nested warpings has been shown to avoid the constraints besetting the former. In the first paper of this series [JHEP 1509 (2015) 202], the Standard Model gauge and fermion fields were extended into such a six-dimensional bulk and the construction was shown to have several interesting and welcome features. In this paper, we discuss the electroweak symmetry breaking, presenting a novel Higgs localization mechanism that leads to interesting phenomenology in the Higgs sector. Localizing the Higgs modifies the $Z_{\mu}$ and $W_{\mu}$ boson wavefunctions, which leads to tree level changes in the oblique parameters. Using these as well as the correction to low-energy four-Fermi operators, we derive the constraints on our model and also discuss the gauge coupling evolution therein. Amusingly, the model can naturally incorporate a Higgs resonance in the 700--800 GeV range.

Bulk gauge and matter fields in nested warping: I. The formalism

The lack of evidence for a TeV-mass graviton has been construed as constricting the Randall-Sundrum model. However, a doubly-warped generalization naturally avoids such restrictions. We develop, here, the formalism for extension of the Standard Model gauge bosons and fermions into such a six-dimensional bulk. Apart from ameliorating the usual problems such as flavour-changing neutral currents, this model admits two very distinct phases, with their own unique phenomenologies.

Supersymmetric gauge theories on five-manifolds

We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. We show that the background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Moreover, we prove that any such metric defines a supersymmetric background. Finally, we construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.

Self-accelerating solutions in the cascading DGP braneworld

Abstract The self-accelerating branch of the Dvali–Gabadadze–Porrati (DGP) five-dimensional braneworld has provided a compelling model for the current cosmic acceleration. Recent observations, however, have not favored it so much. We discuss the solutions which contain a de Sitter 3-brane in the cascading DGP braneworld model, which is a kind of higher-dimensional generalizations of the DGP model, where a p-dimensional brane is placed on a ( p + 1 ) -dimensional one and the p-brane action contains the ( p + 1 ) -dimensional induced scalar curvature term. In the simplest six-dimensional model, we derive the solutions. Our solutions can be classified into two branches, which reduce to the self-accelerating and normal solutions in the limit of the original five-dimensional DGP model. In the presence of the six-dimensional bulk gravity, the ‘normal’ branch provides a new self-accelerating solution. The expansion rate of this new branch is generically lower than that of the original one, which may alleviate the fine-tuning problem.

Self-accelerating solutions in the cascading DGP braneworld

The self-accelerating branch of the Dvali–Gabadadze–Porrati (DGP) five-dimensional braneworld has provided a compelling model for the current cosmic acceleration. Recent observations, however, have not favored it so much. We discuss the solutions which contain a de Sitter 3-brane in the cascading DGP braneworld model, which is a kind of higher-dimensional generalizations of the DGP model, where a p-dimensional brane is placed on a (p+1)-dimensional one and the p-brane action contains the (p+1)-dimensional induced scalar curvature term. In the simplest six-dimensional model, we derive the solutions. Our solutions can be classified into two branches, which reduce to the self-accelerating and normal solutions in the limit of the original five-dimensional DGP model. In the presence of the six-dimensional bulk gravity, the ‘normal’ branch provides a new self-accelerating solution. The expansion rate of this new branch is generically lower than that of the original one, which may alleviate the fine-tuning problem.

The consistency of codimension-2 braneworlds and their cosmology

We study axially symmetric codimension-2 cosmology for adistributional braneworld fueled by a localised four-dimensionalperfect fluid, in a six-dimensional Lovelock theory. We argue thatonly the matching conditions (dubbed topological) where theextrinsic curvature on the brane has no jump describe a purecodimension-2 brane. If there is discontinuity in the extrinsiccurvature on the brane, this induces inevitably codimension-1distributional terms. We study these topological matchingconditions, together with constraints from the bulk equationsevaluated at the brane position, for two cases of regularisation ofthe codimension-2 defect. First, for an arbitrary smoothregularisation of the defect and second for a ring regularisationwhich has a cusp in the angular part of the metric. For acosmological ansatz, we see that in the first case the coupledsystem is not closed and requires input from the bulk equations awayfrom the brane. The relevant bulk function, which is atime-dependent angular deficit, describes the energy exchange between the brane andthe six-dimensional bulk spacetime. On the other hand, for the ringregularisation case, the system is closed and there is no leakage ofenergy in the bulk. We demonstrate that the full set of matchingconditions and field equations evaluated at the brane position areconsistent, correcting some previous claim in the literature whichused rather restrictive assumptions for the form of geometricalquantities close to the codimension-2 brane. We analyse the modifiedFriedmann equation and we see that there are certain corrections coming fromthe non-zero extrinsic curvature on the brane. We establish the presence ofgeometric self-acceleration and apossible curvature domination wedged in between the period of matterand self-acceleration eras as signatures of codimension-2 cosmology.

Properties of codimension-2 braneworlds in six-dimensional Lovelock theory

We consider maximally symmetric 3-branes embedded in a six-dimensional bulk spacetime with Lovelock dynamics. We study the properties of the solutions with respect to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. Some simple solutions are shown to give rise to self-accelerating braneworlds, whereas several others solutions have self-tuning properties. For the case of geometric self-acceleration we argue that the cross-over scale in between four-dimensional and higher-dimensional gravity and the scale of late-time geometric acceleration, fixed by the present horizon size, are related via the conical deficit angle of the six-dimensional bulk solution, which is a free parameter.

Induced gravity on intersecting brane worlds. II. Cosmology

We explore cosmology of intersecting brane worlds with induced gravity on the branes. We find the cosmological equations that control the evolution of a moving codimension-one brane and a codimension-two brane that sits at the intersection. We study the Friedmann equation at the intersection, finding new contributions from the six-dimensional bulk. These higher dimensional contributions allow us to find new examples of self-accelerating configurations for the codimension-two brane at the intersection and we discuss their features.

Self-properties of codimension-2 braneworlds

We consider four-dimensional de Sitter, flat and anti de Sitter branes embedded in a six-dimensional bulk spacetime whose dynamics is dictated by Lovelock theory. We find, applying a generalised version of Birkhoff's theorem, that all possible maximally symmetric braneworld solutions are embedded in Wick-rotated black hole spacetimes of Lovelock theory. These are warped solitonic spaces, where the horizons of the black hole geometries correspond to the possible positions of codimension-2 branes. The horizon temperature is related via conical singularities to the tension or vacuum energy of the branes. We classify the braneworld solutions for certain combinations of bulk parameters, according to their induced curvature, their vacuum energy and their effective compactness in the extra dimensions. The bulk Lovelock theory gives an induced gravity term on the brane, which, we argue, generates four-dimensional gravity up to some distance scale. As a result, some simple solutions, such as the Lovelock corrected Schwarzschild black hole in six dimensions, are shown to give rise to self-accelerating braneworlds. We also find that several other solutions have self-tuning properties. Finally, we present regular gravitational instantons of Lovelock gravity and comment on their significance.

Braneworlds in six dimensions: new models with bulk scalars

Six-dimensional bulk spacetimes with 3- and 4-branes are constructed using certain non-conventional bulk scalars as sources. In particular, we investigate the consequences of having the phantom (negative kinetic energy) and the Brans–Dicke scalar in the bulk while obtaining such solutions. We find geometries with 4-branes with a compact on-brane dimension (hybrid compactification) which may be assumed to be small in order to realize a 3-brane world. On the other hand, we also construct, with similar sources, bulk spacetimes where a 3-brane is located at a conical singularity. Furthermore, we investigate the issue of localization of matter fields (scalar, fermion, graviton, vector) on these 3- and 4-branes and conclude with comments on our six-dimensional models.

The extended ADS/CFT correspondence

The correspondence between conformal covariant fields in Minkowski's space-time and isometric fields in the five dimensional anti-deSitter space-time is extended to a six-dimensional bulk space and its regular sub-manifolds, so as to include the analysis of evaporating Schwarzschild's black holes without loss of quantum unitarity.

A conical tear drop as a vacuum-energy drain for the solution of the cosmological constant problem

We propose a partial solution to the cosmological constant problem by using the simple observation that a three-brane in a six-dimensional bulk is flat. A model is presented in which Standard Model vacuum energy is always absorbed by the transverse space. The latter is a tear-drop like space with a conical singularity, which preserves bulk supersymmetry and gives rise to conventional macroscopic 4D gravity with no cosmological constant. Its cone acts like a drain depleting vacuum energy from the three-brane to the tear drop increasing its volume. We stress that although gravity is treated classically, Standard Model is handled quantum-field theoretically and the model is robust against Standard Model corrections and particular details. The price paid is the presence of boundaries which are nevertheless physically harmless by appropriate boundary conditions.

Semisimple group unification in the supersymmetric brane world

The conventional supersymmetric grand unified theories suffer from two serious problems: the large mass splitting between doublet and triplet Higgs multiplets, and the too long lifetime of the proton. A unification model based on a semisimple group $\mathrm{SU}{(5)}_{\mathrm{GUT}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(3)}_{H}$ has been proposed to solve both of the problems simultaneously. Although the proposed model is perfectly consistent with observations, there are various mysteries. In this paper we show that such mysterious features in the original model are naturally explained by embedding the model into the brane world in a higher-dimensional space-time. In particular, the relatively small gauge coupling constant of the $\mathrm{SU}{(5)}_{\mathrm{GUT}}$ at the unification energy scale is a consequence of a relatively large volume of extra dimensions. Here, we put the $\mathrm{SU}{(5)}_{\mathrm{GUT}}$ gauge multiplet in a six-dimensional bulk and assume all fields in the $\mathrm{U}{(3)}_{H}$ sector to reside on a three-dimensional brane located in the bulk. On the other hand, all chiral multiplets of quarks, leptons, and Higgs bosons are assumed to reside on a 3-brane at a ${\mathbf{T}}^{2}/{\mathbf{Z}}_{4}$ orbifold fixed point. The quasi-$\mathcal{N}=2$ supersymmetry in the hypercolor $\mathrm{U}{(3)}_{H}$ sector is understood as a low-energy remnant of the $\mathcal{N}=4$ supersymmetry in a six-dimensional space-time. We further extend the six-dimensional model to a ten-dimensional theory. Possible frameworks of string theories are also investigated to accommodate the present brane-world model. We find that the type-IIB string theory with a D3-D7 brane structure is an interesting candidate.

Warped Compactification with a Four-Brane

Warped compactification of the six-dimensional bulk with a negative cosmological constant is realized with a 4-brane along with an abelian gauge theory. No fine tuning of couplings are needed to obtain the vanishing cosmological constant in four dimensions, as is the case for the bulk with a positive cosmological constant.