Compact Extra Dimensions Research Articles

On Newton's law in supersymmetric braneworld models

We study the propagation of gravitons within 5-D supersymmetric braneworld models with a bulk scalar field. The setup considered here consists of a 5-D bulk spacetime bounded by two 4-D branes localized at the fixed points of an $S^1/Z_2$ orbifold. There is a scalar field $\phi$ in the bulk which, provided a superpotential $W(\phi)$, determines the warped geometry of the 5-D spacetime. This type of scenario is common in string theory, where the bulk scalar field $\phi$ is related to the volume of small compact extra dimensions. We show that, after the moduli are stabilized by supersymmetry breaking terms localized on the branes, the only relevant degrees of freedom in the bulk consist of a 5-D massive spectrum of gravitons. Then we analyze the gravitational interaction between massive bodies localized at the positive tension brane mediated by these bulk gravitons. It is shown that the Newtonian potential describing this interaction picks up a non-trivial contribution at short distances that depends on the shape of the superpotential $W(\phi)$. We compute this contribution for dilatonic braneworld scenarios $W(\phi) = e^{\alpha \phi}$ (where $\alpha$ is a constant) and discuss the particular case of 5-D Heterotic M-theory: It is argued that a specific footprint at micron scales could be observable in the near future.

Higgs and Wilson lines in field and string theory

This is a short review on basics of the use of the Wilson line to break gauge symmetry in theories with compact extra dimensions. We show how the computation of the one-loop effective field theory leads to a finite result. We then explain the realization of this breaking and the effective potential computation in an open string theory framework with D-branes. To cite this article: K. Benakli, C. R. Physique 8 (2007).

Discrete time evolution and energy nonconservation in noncommutative physics

Time-space noncommutativity leads to quantisation of time [1] and energy nonconservation [2] when time is conjugate to a compact spatial direction like a circle. In this context energy is conserved only modulo some fixed unit. Such a possibility arises for example in theories with a compact extra dimension with which time does not commute. The above results suggest striking phenomenological consequences in extra dimensional theories and elsewhere. In this paper we develop scattering theory for discrete time translations. It enables the calculation of transition probabilities for energy nonconserving processes and has a central role both in formal theory and phenomenology.

Revealing the large extra dimension effective interaction at ane+e−collider with polarized beams

Several types of new physics scenarios are represented by contactlike effective interactions. An example is the exchange of nonstandard quanta of very large mass scales, beyond the kinematical limit for direct production set by the available collider energy. This kind of interactions can be revealed only through deviations of observables from the standard model predictions. If such deviations were observed, the relevant source should be identified among the possible models that could explain them. Here, we assess the expected ``identification reach'' on the ADD model of gravity in large compactified extra dimensions, against the compositeness-inspired four-fermion contact interaction. As basic observables we take the differential cross sections for fermion-pair production at a 0.5\char21{}1 TeV electron-positron linear collider with both beams longitudinally polarized. For the four-fermion contact interaction, we assume a general linear combination of the individual models with definite chiralities, with arbitrary coupling constants. In this sense, the estimated identification reach on the ADD model can be considered as ``model independent.'' In the analysis, we give estimates also for the expected ``discovery reaches'' on the various scenarios. We emphasize the substantial role of beams polarization in enhancing the sensitivity to the contactlike interactions under consideration.

Brane cosmic string compactification in Brans-Dicke theory

We investigate an alternative compactification of extra dimensions using local cosmic string in the Brans-Dicke gravity framework. In the context of dynamical systems it is possible to show that there exist a stable field configuration for the Einstein-Brans-Dicke equations. We explore the analogies between this particular model and the Randall-Sundrum scenario.

Quark-lepton symmetry in five dimensions

We construct a complete five dimensional quark-lepton symmetric model, with all fields propagating in the bulk. The extra dimension forms an ${S}^{1}/{Z}_{2}\ifmmode\times\else\texttimes\fi{}{Z}_{2}^{\ensuremath{'}}$ orbifold with the zero mode fermions corresponding to standard model quarks localized at one fixed point. Zero modes corresponding to left (right)-chiral leptons are localized at (near) the other fixed point. This localization pattern is motivated by the symmetries of the model. Shifting the right-handed neutrinos and charged leptons slightly from the fixed point provides a new mechanism for understanding the absence of relations of the type ${m}_{e}={m}_{u}$ or ${m}_{e}={m}_{d}$ in quark-lepton symmetric models. Flavor changing neutral currents resulting from Kaluza-Klein gluon exchange, which typically arise in the quark sector of split fermion models, are suppressed due to the localization of quarks at one point. The separation of quarks and leptons in the compact extra dimension also acts to suppress the proton decay rate. This permits the extra dimension to be much larger than that obtained in a previous construct, with the bound $1/R\ensuremath{\gtrsim}30\text{ }\text{ }\mathrm{TeV}$ obtained.

The A5 and the pion field

In this talk, an SU ( N f ) × SU ( N f ) Yang-Mills model with a compact extra-dimension is used to describe the spin-1 mesons and pions of massless QCD in the large- N c . The right 4D symmetry and symmetry-breaking pattern is produced by imposing appropriate boundary conditions. The Goldstone boson (GB) fields are constructed using a Wilson line. We derive the low-energy limit (chiral lagrangian), discuss ρ -meson dominance, sum rules between resonance couplings and the relation with the QCD high-energy behavior. Finally, we provide an analytic expression for the two-point function of vector and axial currents.

Index Theorem in Finite Noncommutative Geometry

Noncommutative (NC) geometry is interesting since it is related to string theories and matrix models,1)–3) and it may capture some nature of quantum gravity. It is also a candidate for a new regularization of quantum field theory.4) Study about topological aspects of gauge theory on it is important since compactification of extra dimensions with nontrivial index in string theory can realize chiral gauge theory in our spacetime. Ultimately, we hope to realize such a mechanism dynamically, for instance, in IIB matrix model5) where spacetime structure has been studied intensively.6),7) Unusual properties of NC geometry may also provide a solution of strong CP problem and baryon asymmetry of the universe. Index theorem plays a key role in these studies. While it can be proved in theories with infinite degrees of freedom,8),9) it becomes a nontrivial issue in finite cases. This problem was solved in lattice gauge theory by using Ginsparg-Wilson (GW) relation,10)–13) and this idea has been successfully extended to the NC geometry. We have provided a general prescription to construct a GW Dirac operator with coupling to non-vanishing gauge field backgrounds on general finite NC geometries.14) Owing to the GW relation, an index theorem can be proved even for finite NC geometries. The index takes only integer values by construction, and it is shown to become the corresponding topological charge as the number of degrees of freedom is properly taken to infinity. While explicit construction has been provided for the fuzzy 2sphere14),15) and for the NC torus,16),17) it is possible for other cases, which will be reported in future publication. As a topologically nontrivial configuration on the fuzzy 2-sphere, we constructed ’t Hooft-Polyakov (TP) monopole configuration.18),19) We further presented a mechanism for dynamical generation of a nontrivial index, by showing that the TP monopole configurations are stabler than the topologically trivial sector in the YangMills-Chern-Simons matrix model.20) However, in order to obtain non-zero indices for these configurations, one needs to introduce a projection operator in the definition of the index. We gave an interpretation for the projection operator, and extended the index theorem to general configurations which do not necessarily satisfy the equation of motion.21) Since the U(2) gauge theory on the fuzzy sphere

Suppressing proton decay by separating quarks and leptons

Arkani-Hamed and Schmaltz have shown that proton stability need not originate from symmetries in a high energy theory. Instead the proton decay rate is suppressed if quarks and leptons are spatially separated in a compact extra dimension. This separation may be achieved by coupling five-dimensional fermions to a bulk scalar field with a nontrivial vacuum profile and requires relationships between the associated quark and lepton Yukawa couplings. We hypothesize that these relationships are the manifestation of an underlying symmetry. We further show that the Arkani-Hamed and Schmaltz proposal may suggest that proton stability is the result of an underlying symmetry, though not necessarily the traditional baryon number symmetry. © 2006 The American Physical Society.

Consistent ADD scenario with stabilized extra dimension

A model with one compact extra dimension and a scalar field of Brans-Dicke type in the bulk is discussed. It describes two branes with non-zero tension embedded into the space-time with flat background. This setup allows one to use a very simple method for stabilization of the size of extra dimension. It appears that the four-dimensional Planck mass is expressed only through parameters of the scalar field potentials on the branes.

Measuring the shape of the extra dimension

We study the possibility of extracting geometric information on the shape of the extra dimension from four-dimensional data such as the mass of the Kaluza-Klein (KK) mode. Assuming one compact extra dimension whose geometry can be considered as perturbations in the flat background, we show that if there is a Z2 symmetry in the extra dimension, for example the KK parity in models with Universal Extra Dimensions, then the warp factor in the metric is completely determined by the KK mass alone. Without KK parity, additional information depending on the boundary conditions is needed to fully reconstruct the metric, even though such information may be experimentally challenging to obtain. The case in a general background geometry is also considered.

Gravitational diffraction radiation

We show that if the visible universe is a membrane embedded in a higher-dimensional space, particles in uniform motion radiate gravitational waves because of spacetime lumpiness. This phenomenon is analogous to the electromagnetic diffraction radiation of a charge moving near to a metallic grating. In the gravitational case, the role of the metallic grating is played by the inhomogeneities of the extra-dimensional space, such as a hidden brane. We derive a general formula for gravitational diffraction radiation and apply it to a higher-dimensional scenario with flat compact extra dimensions. Gravitational diffraction radiation may carry away a significant portion of the particle's initial energy. This allows to set stringent limits on the scale of brane perturbations. Physical effects of gravitational diffraction radiation are briefly discussed.

Probing the Randall-Sundrum geometric origin of flavor with lepton flavor violation

The anarchic Randall-Sundrum model of flavor is a low energy solution to both the electroweak hierarchy and flavor problems. Such models have a warped, compact extra dimension with the standard model fermions and gauge bosons living in the bulk, and the Higgs living on or near the TeV brane. In this paper we consider bounds on these models set by lepton flavor-violation constraints. We find that loop-induced decays of the form l{yields}l{sup '}{gamma} are ultraviolet sensitive and incalculable when the Higgs field is localized on a four-dimensional brane; this drawback does not occur when the Higgs field propagates in the full five-dimensional space-time. We find constraints at the few TeV level throughout the natural range of parameters, arising from {mu}-e conversion in the presence of nuclei, rare {mu} decays, and rare {tau} decays. A tension exists between loop-induced dipole decays such as {mu}{yields}e{gamma} and tree-level processes such as {mu}-e conversion; they have opposite dependences on the five-dimensional Yukawa couplings, making it difficult to decouple flavor-violating effects. We emphasize the importance of the future experiments MEG and PRIME. These experiments will definitively test the Randall-Sundrum geometric origin of hierarchies in the lepton sector at the TeV scale.

QUANTUM PERFECT-FLUID KALUZA–KLEIN COSMOLOGY

The perfect-fluid cosmology in the (1+d+D)-dimensional Kaluza–Klein space–times for an arbitrary barotropic equation of state p = (γ-1)ρ is quantized by using the Schutz's variational formalism. We make efforts in the mathematics to solve the problems in two cases. In the first case of the stiff fluid γ = 2 we exactly solve the Wheeler–DeWitt equation when the d space is flat. After the superposition of the solutions the wave-packet function is obtained exactly. We analyze the Bohmian trajectories of the final-stage wave-packet functions and show that the scale functions of the flat d spaces and the compact D spaces will eventually evolve into the nonzero finite values. In the second case of γ≈2, we use the approximated wave function in the Wheeler–DeWitt equation to find the analytic forms of the final-stage wave-packet functions. After analyzing the Bohmian trajectories we show that the flat d spaces will be expanding forever while the scale function of the contracting D spaces would not become zero within finite time. Our investigations indicate that the quantum effect in the quantum perfect-fluid cosmology could prevent the extra compact D spaces in the Kaluza–Klein theory from collapsing into a singularity or that the "crack-of-doom" singularity of the extra compact dimensions is made to occur at t = ∞.

Kaluza-Klein Black Holes with Squashed Horizons

We study geometrical structures of charged static black holes in the five-dimensional Einstein-Maxwell theory. The black holes we study have horizons in the form of squashed $ {\rm S}^3$, and their asymptotic structure consists of a twisted ${\rm S}^1$ bundle over the four-dimensional flat spacetime at the spatial infinity. The spacetime we consider is fully five-dimensional in the vicinity of the black hole and four-dimensional with a compact extra dimension at infinity.

Collider implications of multiple nonuniversal extra dimensions

We consider multiple TeV scale extra compact dimensions in an asymmetric string compactification scenario in which the SM gauge bosons can propagate into the TeV scale extra dimensions while the SM fermions are confined to the usual SM D3 brane. We calculate the contributions that the KK excitations of the gluons make to the multijet cross sections in proton proton collisions at the LHC energy. At very high pT, the dijet signal will either be enhanced significantly due to virtual g star exchanges or place a lower bound on the compactification scale of about 8 TeV. We find that the dijet signal is very sensitive to three parameters: the compactification scale, the string scale, and the number of extra dimensions. Thus, although the dijet signal is much more sensitive to KK effects, the dijet signal alone does not provide sufficient information to deduce the number of extra dimensions nor the compactification scale. However, the three jet signal, which is not sensitive to the string scale, can be analyzed in conjunction with the dijet signal to extract all three parameters. For proton proton collisions at the LHC energy, the three jet signal can be significantly enhanced by KK contributions for a compactification scale of about 4 to 5 TeV.

COSMOLOGICAL CONSTANT PROBING SHAPE MODULI THROUGH LARGE EXTRA DIMENSIONS

We consider a compactification of extra dimensions and numerically calculate Casimir energy which is provided by the mass of Kaluza–Klein modes. For the extra space we consider a torus with shape moduli and show that the corresponding vacuum energy is represented as a function of the moduli parameter of the extra dimensions. By assuming that the Casimir energy may be identified with cosmological constant, we evaluate the size of extra dimensions in terms of the recent data given by the Wilkinson Microwave Anisotropy Probe (WMAP) measurement and the supernovae observations. We suggest that the observed cosmological constant may probe the shape moduli of the extra space by the study of the Casimir energy of the compactified extra dimensions.

Fixed points of quantum gravity in extra dimensions

We study quantum gravity in more than four dimensions with renormalisation group methods. We find a non-trivial ultraviolet fixed point in the Einstein-Hilbert action. The fixed point connects with the perturbative infrared domain through finite renormalisation group trajectories. We show that our results for fixed points and related scaling exponents are stable. If this picture persists at higher order, quantum gravity in the metric field is asymptotically safe. We discuss signatures of the gravitational fixed point in models with low scale quantum gravity and compact extra dimensions.

Dark energy, scalar-tensor gravity, and large extra dimensions

We explore in detail a dilatonic scalar-tensor theory of gravity inspired by large extra dimensions, where a radion field from compact extra dimensions gives rise to quintessence in our 4-dimensional world. We show that the model can give rise to other types of cosmologies as well, some more akin to k-essence and possibly variants of phantom dark energy. In our model the field (or radius) stabilization arises from quantum corrections to the effective 4D Ricci scalar. We then show that various constraints nearly determine the model parameters, and give an example of a quintessence-type cosmology consistent with observations. We show that the upcoming SNAP-experiment would easily distinguish the present model from a constant {lambda} model with an equal amount of dark energy, but that the SNAP-data alone will not be able distinguish it from a {lambda} model with about 5% less dark energy.

Experimentally probing the shape of extra dimensions

Theories with compact extra dimensions have become increasingly popular. In some theories the standard model particles are confined to our four-dimensional world and only gravity can propagate in the extra dimensions. In these models the size of the extra dimensions can be as large as hundreds of microns. The functional dependence of the gravitational force on distance is well known at both large and small distances compared to the size of the extra dimensions; for two extra dimensions, for example, it varies from 1∕r2 to 1∕r4 as the distance decreases. However, the dependence for intermediate distances has not been fully calculated. We determine this dependence as a function of both the size of the extra dimensions and the possible angle between the extra dimensional unit vectors and show that high precision measurements of the gravitational force would make possible the determination of the shape of the extra dimensions.