Algebraic Geometry Approach in Theories with Extra Dimensions II. Tensor Length Scale, Compactification and Rescaling
Bogdan G. Dimitrov
备注：
21 pages; this is a part of the former hep-th/0511136, but with a new "Discussion" part and also Appendices A and B; also minor corrections and changes in the text and in the enumeration of the formulaes; subm. to Gen. Rel. Grav
In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor components. Then the notion of "compactification" in low energy type I string theory is supplemented by the operation of "rescaling" of the contravariant metric components. For both the cases of "rescaling + compactification" and "compactification + rescaling", quasilinear differential equations in partial derivatives have been obtained and the corresponding solutions have been found for the scale (length) function and for the case of a flat 4D Minkowski space, embedded into a 5D space with an exponential warp factor. A differential equation has been obtained and investigated also from the equality of the "rescaled" scalar curvature with the usual one.
Recently there have been discussions about which complex metrics should be allowable in quantum gravity. These discussions assumed that the matter fields were real valued. We make the observation that for compactified solutions it makes sense to demand convergence of the theory's path integral in the higher-dimensional parent theory. Upon compactification this allows for more general matter configurations in the lower-dimensional theory, in particular it allows for complex scalar fields, with a bound on their imaginary parts. Similar considerations apply to metric rescalings in the presence of…
The Riemannian geometry of coset spaces is reviewed, with emphasis on its applications to supergravity and M-theory compactifications. Formulae for the connection and curvature of rescaled coset manifolds are generalized to the case of nondiagonal Killing metrics. The example of the N^{010} spaces is discussed in detail. These are a subclass of the coset manifolds N^{pqr}=G/H = SU(3) x U(1)/U(1) x U(1), the integers p,q,r characterizing the embedding of H in G. We study the realization of N^{010} as G/H=SU(3) x SU(2)/U(1) x SU(2) (with diagonal embedding of the SU(2) \in H into G). For a parti…
On the base of the distinction between covariant and contravariant metric tensor components, an approach from algebraic geometry will be proposed, aimed at finding new solutions of the Einstein's equations both in GTCCCM and in standard gravity theory, if these equations are treated as algebraic equations. As a partial case, some physical applications of the approach have been considered in reference to theories with extra dimensions. The s.c. "length function" l(x) has been introduced and has been found as a solution of quasilinear differential equations in partial derivatives for two differe…
On the base of the distinction between covariant and contravariant metric tensor components, a new (multivariable) cubic algebraic equation for reparametrization invariance of the gravitational Lagrangian has been derived and parametrized with complicated non - elliptic functions, depending on the (elliptic) Weierstrass function and its derivative. This is different from standard algebraic geometry, where only two-dimensional cubic equations are parametrized with elliptic functions and not multivariable ones. Physical applications of the approach have been considered in reference to theories w…
In this work, we use the Casimir effect to probe the existence of one extra dimension. We begin by evaluating the Casimir pressure between two plates in a $M^4\times S^1$ manifold, and then use an appropriate statistical analysis in order to compare the theoretical expression with a recent experimental data and set bounds for the compactification radius.
We identify instantons representing vacuum decay in a 6-dimensional toy model for string theory flux compactifications, with the two extra dimensions compactified on a sphere. We evaluate the instanton action for tunneling between different flux vacua, as well as for the decompactification decay channel. The bubbles resulting from flux tunneling have an unusual structure. They are bounded by two-dimensional branes, which are localized in the extra dimensions. This has important implications for bubble collisions.
This thesis analyses gauged supergravities in various dimensions and their possible origin from compactifications of string theory. In the effective description the fluxes appear in the theory as deformation parameters generating a potential for the scalar fields. Physics after compactification is only sensitive to the orbits of the global symmetry group, in that gaugings lying in the same orbit are related by duality transformations. Given a certain gauged supergravity containing non-geometric fluxes, we discuss in dimension seven and higher whether there exists a duality transformation that …
It has recently been proposed that gravity-localized compactifications can generate the required gauge hierarchy without the need for hierarchically large extra spacetime dimensions. In this paper, we show that gauge coupling unification arises naturally in such scenarios as a result of the anomaly induced by the rescaling of the wavefunctions of the brane fields. Thus, ``anomaly-induced'' gauge coupling unification can easily explain the apparent low-energy gauge couplings in gravity-localized compactifications. However, we also point out a number of phenomenological difficulties with such co…
We investigate multidimensional gravity with the Gauss-Bonnet term and with torsion on the space of extra dimensions chosen to be the group manifold of a simple Lie group. We take the Robertson-Walker ansatz for the 4-dimensional space-time and study the potential of a dilaton and torsion fields. It is shown that for certain values of the parameters of the initial theory the potential has classically stable minima, corresponding to the spontaneous compactification of the extra dimensions. However, these minima have zero torsion.
We investigate a simple extra-dimensional model and its four-dimensional vacua. This model has a two-form flux and a positive cosmological constant, and the extra dimensions are compactified as the product of $N$ two-spheres. The theory is an interesting laboratory because it is at once simple enough to be soluble but rich enough to exhibit many features not present in previous model landscapes.
The type IIB matrix model is conjectured to be a nonperturbative definition of type IIB superstring theory. In this model, spacetime is a dynamical quantity and compactification of extra dimensions can be realized via spontaneous symmetry breaking(SSB). In this work, we consider a simpler, related, six dimensional model in its Euclidean version and study it numerically. Our calculations provide evidence that the SO(6) rotational symmetry of the model breaks down to SO(3), which means that the theory lives in a vacuum where 3 out of the 6 dimensions are large compared to the other 3. Our result…
We study the Gregory-Laflamme instability of a large uniform black brane wrapping a two-sphere compactification manifold. This paper extends the work arXiv:hep-th/0604015, where the compactifications on p-torus were considered. The new features of the spherical case are the non-zero curvature of the compactification manifold and the absence of the rescaling symmetry due to a built-in stabilization mechanism. We calculate the order of the phase transition in dependence on the number d of extended dimensions using the Landau-Ginzburg approach. It is found that for d > 11 a uniform spherical blac…
We construct supergravity backgrounds representing non-homogeneous compactifications of d=10,11 supergravities to four dimensions, which cannot be written as a direct product. The geometries are regular and approach $AdS_7\times S^4$ or $AdS_5\times S^5$ at infinity; they are generically non-supersymmetric, except in a certain "extremal" limit, where a Bogomol'nyi bound is saturated and a naked singularity appears. By using these spaces, one can construct a model of QCD that generalizes by one (or two) extra parameters a recently proposed model of QCD based on the non-extremal D4 brane. This a…
We consider `brane universe' scenarios with standard-model fields localized on a 3-brane in 6 spacetime dimensions. We show that if the spacetime is rotationally symmetric about the brane, local quantities in the bulk are insensitive to the couplings on the brane. This potentially allows compactifications where the effective 4-dimensional cosmological constant is independent of the couplings on the 3-brane. We consider several possible singularity-free compactification mechanisms, and find that they do not maintain this property. We also find solutions with naked spacetime singularities, and w…
Expressions for the thermodynamic potential of a Dirac fermion gas are represented at finite temperature with the chemical potential in an ultrastatic space $R^d\times S^N$. The high- and low- temperature expansions for the thermodynamic potential are obtained and, in particular, strongly degenerate fermi gas is investigated. For the Candelas-Weinberg model, sufficiently high "charge" density prevents the compactification of the extra space.
We conjecture that the extra dimensions are physical non-compact at high energy scale or high temperature; after the symmetry breaking or cosmological phase transition, the bulk cosmological constant may become negative, and then, the extra dimensions may become physical compact at low energy scale. We show this in a five-dimensional toy brane model with three parallel 3-branes and a real bulk scalar whose potential is temperature dependent. We also point out that after the global or gauge symmetry breaking, or the supersymmetry breaking in supergravity theory, the spontaneous physical compact…
In this paper we derive a formula for the energy loss due to elastic N to N particle scattering in models with extra dimensions that are compactified on a radius R. In contrast to a previous derivation we also calculate additional terms that are suppressed by factors of frequency over compactification radius. In the limit of a large compactification radius R those terms vanish and the standard result for the non compactified case is recovered.
Kaluza-Klein compactifications with four-dimensional inflationary geometry combine the attractive idea of higher dimensional models with the attempt to incorporate four-dimensional early-time or late-time cosmology. We analyze the mass spectrum of cosmological perturbations around such compactifications, including the scalar, vector, and tensor sector. Whereas scalar perturbations were discussed before, the spectrum of vector and tensor perturbations is a new result of this article. Moreover, the complete analysis shows, that possible instabilities of such compactifications are restricted to t…
We propose a new mechanism of spontaneous supersymmetry breaking. The existence of extra dimensions with nontrivial topology plays an important role. We investigate new features resulting from this mechanism. One noteworthy feature is that there exists a phase in which the translational invariance for the compactified directions is broken spontaneously. The mechanism we propose also yields quite different vacuum structures for models with different global symmetries.
The possibility of neutral, brane-like solutions in a higher dimensional setting is discussed. In particular, we describe a supersymmetric solution in six dimensions which can be interpreted as a "three-brane" with a non-compact transverse space of finite volume. The construction can be generalized to n+4-dimensions and the result is a n+3-brane compactified on a n-1-dimensional Einstein manifold with a non-compact extra dimension. We find that there always exists a massless graviton trapped in four-dimensions while a bulk abelian gauge field gives rise to a unique four-dimensional massless ph…
We consider a six-dimensional braneworld model and we study the cosmological evolution of a (4+1) brane-universe. Introducing matter on the brane we show that the scale factor of the physical three-dimensional brane-universe is related to the scale factor of the fourth dimension on the brane, and the suppression of the extra dimension compared to the three dimensions requires the presence of dark energy.
In M(atrix) theory, there exist membranes and longitudinal 5-branes (L5-branes) as extended objects. Transverse components of these brane solutions are known to be described by fuzzy CP^k (k=1,2), where k=1 and k=2 correspond to spherical membranes and L5-branes of CP^2 \times S^1 world-volume geometry, respectively. In addition to these solutions, we here show the existence of L7-branes of CP^3 \times S^1 geometry, introducing extra potentials to the M(atrix) theory Lagrangian. As in the cases of k=1,2, the L7-branes (corresponding to k=3) also break the supersymmetries of M(atrix) theory. Th…
We consider how accelerated expansion, whether due to inflation or dark energy, imposes strong constraints on fundamental theories obtained by compactification from higher dimensions. For theories that obey the null energy condition (NEC), we find that inflationary cosmology is impossible for a wide range of compactifications; and a dark energy phase consistent with observations is only possible if both Newton's gravitational constant and the dark energy equation-of-state vary with time. If the theory violates the NEC, inflation and dark energy are only possible if the NEC-violating elements a…
By studying the effects of the shape moduli associated with toroidal compactifications, we demonstrate that Planck-sized extra dimensions can cast significant ``shadows'' over low-energy physics. These shadows can greatly distort our perceptions of the compactification geometry associated with large extra dimensions, and place a fundamental limit on our ability to probe the geometry of compactification simply by measuring Kaluza-Klein states. We also discuss the interpretation of compactification radii and hierarchies in the context of geometries with non-trivial shape moduli. One of the main …
Perturbative breaking of supersymmetry in four-dimensional string theories predict in general the existence of new large dimensions at the TeV scale. Such dimensions can be consistent with perturbative unification up to the Planck scale in a class of string models and open the exciting possibility of lowering a part of the massive string spectrum at energies accessible to future accelerators. The main signature is the production of Kaluza-Klein excitations which have a very particular structure, strongly correlated with the supersymmetry breaking mechanism. We present a model independent analy…
Possible experimental manifestations of the contribution of heavy Kaluza-Klein particles, within a simple scalar model in six dimensions with spherical compactification, are studied. The approach is based on the assumption that the inverse radius $L^{-1}$ of the space of extra dimensions is of the order of the scale of the supersymmetry breaking $M_{SUSY} \sim 1 ÷10$ TeV. The total cross section of the scattering of two light particles is calculated to one loop order and the effect of the Kaluza-Klein tower is shown to be noticeable for energies $\sqrt{s} \geq 1.4 L^{-1}$.
In this thesis we study string compactifications on manifolds equipped with a $G$-structure, placing a special emphasis on the interplay between geometry and physics. We follow two complementary approaches. In the first part of the thesis we adopt a sigma model perspective and focus on the worldsheet superconformal field theory. We consider compactifications on 7-dimensional Extra Twisted Connected Sum (ETCS) G$_2$ manifolds as well as 8-dimensional Generalized Connected Sum (GCS) Spin(7) manifolds. We find that the geometric construction is reproduced in the worldsheet algebra via a diamond o…
We construct a simple AdS_4 x S^1 flux compactification stabilized by a complex scalar field winding the extra dimension and demonstrate an instability via nucleation of a bubble of nothing. This occurs when the Kaluza -- Klein dimension degenerates to a point, defining the bubble surface. Because the extra dimension is stabilized by a flux, the bubble surface must be charged, in this case under the axionic part of the complex scalar. This smooth geometry can be seen as a de Sitter topological defect with asymptotic behavior identical to the pure compactification. We discuss how a similar cons…
We study a $(4+D)$-dimensional Kaluza-Klein cosmology with a Robertson-Walker type metric having two scale factors $a$ and $R$, corresponding to $D$-dimensional internal space and 4-dimensional universe, respectively. By introducing an exotic matter as the space-time part of the higher dimensional energy-momentum tensor, a 4-dimensional decaying cosmological term is appeared as $Λ\sim R^{-2}$, playing the role of an evolving dark energy in the universe. The resulting field equations yield the exponential solutions for the scale factors. These exponential behaviors may account for the dynamical…
We point out a simple realization of gauge symmetry enhancement by Wilson lines in QFT with twisted compactification in extra dimensions. We illustrate this in the field contents taken from heterotic supergravity in arbitrary dimensions toroidally compactified.
It is known that spatial curvature can stabilize extra dimensions in Lovelock gravity. In the present paper we study stability of the stabilization solutions in 3-d order Lovelock gravity. We show that in the case of negative spatial curvature of extra dimension space the stabilization solution is always stable. On the contrary, for positive spatial curvature the stability depends on the coupling constant values.
We study in detail certain brane solutions with compact extra dimensions M^4 x K in the IKKT matrix model, with K being a two-dimensional rotating torus embedded in R^6. We focus on the compactification moduli and the fluctuations of K \subset R^6 and their physical significance. Mediated by the Poisson tensor, they contribute to the effective 4-dimensional metric on the brane, and thereby become gravitational degrees of freedom. We show that the zero modes corresponding to the global symmetries of the model lead to Ricci-flat 4-dimensional metric perturbations, wherever the energy-momentum te…
It has been shown that, by adding an extra free field that decouples from the dynamics, one can construct actions for interacting 2n-form fields with self-dual field strengths in 4n+2 dimensions. In this paper we analyze canonical formulation of these theories, and show that the resulting Hamiltonian reduces to the sum of two Hamiltonians with independent degrees of freedom. One of them is free and has no physical consequence, while the other contains the physical degrees of freedom with the desired interactions. For the special cases of chiral scalars in two dimensions and chiral two form fie…
We propose a model of bimetric gravity in which the mixing of metrics naturally gives a mass to a graviton by the compactification with flux of two gauge fields in extra dimensions. We assume that each metric in the solution for the background geometry describes the four-dimensional Minkowski spacetime with an $S^2$ extra space, though the two radii of $S^2$ for two metrics take different values in general. The solution is derived by the effective potential method in the presence of the magnetic fluxes on the extra spheres. We find that the a massive graviton is governed by the Fierz-Pauli Lag…
We discuss the structure of general Anisotropic Compactification in Type I D=4, N=1 string theory. It is emphasized that, in this context, a possible interpretation of M_{Planck} as ``dual'' to (at least) one of the Kaluza-Klein or Windings Modes could provide interesting interpretations of the ``physical scales'' and the GUT coupling. Some of the scenarios presented here are strictly connected with the phenomenological proposal of TeV-scale gravity (i.e. millimiter compactification). We show that in this scenario new and probably dominant effects should arise from the presence of ``low-energy…
We analyze the classical stable configurations of an extra-dimensional gauge theory, in which the extra dimensions are compactified on a torus. Depending on the particular choice of gauge group and the number of extra dimensions, the classical vacua compatible with four-dimensional Poincaré invariance and zero instanton number may have zero energy. For SU(N) on a two-dimensional torus, we find and catalogue all possible degenerate zero-energy stable configurations in terms of continuous or discrete parameters, for the case of trivial or non-trivial 't Hooft non-abelian flux, respectively. We t…
Multilocalization provides a simple way of decoupling the mass scale of new physics from the compactification scale of extra dimensions. It naturally appears, for example, when localization of fermion zero modes is used to explain the observed fermion spectrum, leaving low energy remnants of the geometrical origin of the fermion mass hierarchy. We study the phenomenology of the simplest five dimensional model with order one Yukawa couplings reproducing the standard fermion masses and mixing angles and with a light Kaluza-Klein quark Q_{2/3} saturating experimental limits on V_{tb} and m_Q, and…
We calculate one-loop corrections to the mass for the zero mode of scalar field in a six-dimensional Yang-Mills theory compactified on a torus with magnetic flux. It is shown that these corrections are exactly cancelled thanks to a shift symmetry under the translation in extra spaces. This result is expected from the fact that the zero mode of scalar field is a Nambu-Goldstone boson of the translational invariance in extra spaces.
We consider an eight-dimensional Einstein-Yang-Mills theory to explore whether Yang-Mills instantons formed in extra dimensions can induce the dynamical instability of our four-dimensional spacetime. We show that the Yang-Mills instantons in extra dimensions can trigger the expansion of our universe in four-dimensional spacetime as well as the dynamical compactification of extra dimensions. We also discuss a possibility to realize a reheating mechanism via the quantum back-reaction from the contracting tiny internal space with a smeared instanton.
We consider a toroidal extra-dimensional space with shape moduli $θ$ which is the angle between the two large extra dimensions $R_1$ and $R_2$ (twisted LED with $δ=2$). The Kaluza-Klein (KK) compactification results in a tower of KK bulk neutrinos which are sterile in nature and couple to the active neutrinos in the brane. The active-sterile mixing probability strongly depends on the angle $θ$ due to changing pattern of KK mass gaps which leads to level crossing. Considering only the first two lowest KK states in analogy with $(3+2)$ model, it is shown that $|U_{α4}| > |U_{α5}|$ when $θ= π/2$ …
Many theories beyond the Standard Model include extra dimensions, though these have yet to be directly observed. In this work we consider the possibility of a compactification mechanism which both allows extra dimensions and is compatible with current observations. This compactification is predicted to leave a signature on the CMB by altering the amplitude of the low l multipoles, dependent on the amount of inflation. Recently discovered CMB anomalies at low multipoles may be evidence for this. In our model we assume the spacetime is the product of a four-dimensional spacetime and flat extra d…
The IIB matrix model has been proposed as a non-perturbative definition of superstring theory. In this work, we study the Euclidean version of this model in which extra dimensions can be dynamically compactified if a scenario of spontaneously breaking the SO(10) rotational symmetry is realized. Monte Carlo calculations of the Euclidean IIB matrix model suffer from a very strong complex action problem due to the large fluctuations of the complex phase of the Pfaffian which appears after integrating out the fermions. We employ the factorization method in order to achieve effective sampling. We r…
We discuss role of partially gravitating scalar fields, scalar fields whose energy-momentum tensors vanish for a subset of dimensions, in dynamical compactification of a given set of dimensions. We show that the resulting spacetime exhibits a factorizable geometry consisting of usual four-dimensional spacetime with full Poincare invariance times a manifold of extra dimensions whose size and shape are determined by the scalar field dynamics. Depending on the strength of its coupling to the curvature scalar, the vacuum expectation value (VEV) of the scalar field may or may not vanish. When its V…
We study conformal theories of gravity, i.e. those whose action is invariant under the local transformation g_{μν} -> ω^2 (x) g_{μν}. As is well known, in order to obtain Einstein gravity in 4D it is necessary to introduce a scalar compensator with a VEV that spontaneously breaks the conformal invariance and generates the Planck mass. We show that the compactification of extra dimensions in a higher dimensional conformal theory of gravity also yields Einstein gravity in lower dimensions, without the need to introduce the scalar compensator. It is the field associated with the size of the extra…
It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact spaces of constant curvature, General Relativity is recovered within certain class of Lovelock theories possessing necessarily cubic or higher order terms in curvature. This bounds the higher dimension to be at least seven. Remarkably, the effective gauge coupling and Newton constant in four dimensions are not proportional to the gravitational constant in hig…
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.
We investigate the flux compactification mechanism in simple toy models of Einstein-Born-Infeld theories. These are the direct generalizations of the Einstein-Maxwell flux compactifications that recently gained fame as a toy model for tunneling in the landscape. Our investigation reveals that the Born-Infeld form does not significantly modify the qualitative result of the Einstein-Maxwell theory. for the case of Einstein-Higgs theory, however, we found that the effect of Born-Infeld nonlinearity is to render all q>1 extradimensional compactification unstable against semiclassical tunneling to …
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.
In this paper we study dynamical compactification in Einstein-Gauss-Bonnet gravity from arbitrary dimension for generic values of the coupling constants. We showed that, when the curvature of the extra dimensional space is negative, for any value of the spatial curvature of the four dimensional space-time one obtains a realistic behavior in which for asymptotic time both the volume of the extra dimension and expansion rate of the four dimensional space-time tend to a constant. Remarkably, this scenario appears within the open region of parameters space for which the theory does not admit any m…
The type IIB matrix model, also known as the IKKT matrix model, is a promising candidate for a nonperturbative formulation of superstring theory. In this talk we study the Euclidean version of the IKKT matrix model, which has a "sign problem" due to the Pfaffian coming from integrating out the fermionic degrees of freedom. To study the spontaneous breaking of the SO(10) rotational symmetry, we apply the Complex Langevin Method (CLM) to the Euclidean IKKT matrix model. We conclude that the SO(10) symmetry is broken to SO(3), in agreement with the previous studies by the Gaussian Expansion Metho…
We consider a class of generalized FRW type metrics in the context of higher dimensional Einstein gravity in which the extra dimensions are allowed to have different scale factors. It is shown that noncommutativity between the momenta conjugate to the internal space scale factors controls the power-law behavior of the scale factors in the extra dimensions, taming it to an oscillatory behavior. Hence noncommutativity among the internal momenta of the mini-super-\emph{phase}-space can be used to explain stabilization of the compactification volume of the internal space in a higher dimensional gr…
We show that the bound from the electroweak data on the size of extra dimensions accessible to all the standard model fields is rather loose. These "universal" extra dimensions could have a compactification scale as low as 300 GeV for one extra dimension. This is because the Kaluza-Klein number is conserved and thus the contributions to the electroweak observables arise only from loops. The main constraint comes from weak-isospin violation effects. We also compute the contributions to the S parameter and the $Zb\bar{b}$ vertex. The direct bound on the compactification scale is set by CDF and D…
Supersymmetry breaking and compactification of extra space-time dimensions may have a common dynamical origin if our universe is spontaneously generated in the form of a four-dimensional topological or non-topological defect in higher dimensional space-time. Within such an approach the conventional particles are zero modes trapped in the core of the defect. In many cases solutions of this type spontaneously break all supersymmetries of the original theory, so that the low-energy observer from ``our'' universe inside the core would not detect supersymmetry. Since the extra dimensions are not co…
We give a prescription to add the gravitational field of a global topological defect to a solution of Einstein's equations in an arbitrary number of dimensions. We only demand that the original solution has a O(n) invariance with n greater or equal 3. We will see that the general effect of a global defect is to introduce a deficit solid angle. We also show how the same kind of scalar field configurations can be used for spontaneous compactification of "n" extra dimensions on an n-sphere.
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 propose a new way to hide extra dimensions without invoking branes, based on Lorentz-violating tensor fields with expectation values along the extra directions. We investigate the case of a single vector ``aether'' field on a compact circle. In such a background, interactions of other fields with the aether can lead to modified dispersion relations, increasing the mass of the Kaluza-Klein excitations. The mass scale characterizing each Kaluza-Klein tower can be chosen independently for each species of scalar, fermion, or gauge boson. No small-scale deviations from the inverse square law for…
Effects of Kaluza-Klein excitations associated with extra dimensions with large radius compactifications on the Fermi constant are explored. It is shown that the current precision determinations of the Fermi constant, of the fine structure constant, and of the W and Z mass put stringent constraints on the compactification radius. The analysis excludes one extra space time dimension below $\sim 1.6$ TeV, and excludes 2, 3 and 4 extra space dimensions opening simultaneously below $\sim$ 3.5 TeV, 5.7 TeV and 7.8 TeV at the $90% CL$. Implications of these results for future collider experiments ar…
A SU(3) \times SU(2) \times U(1) supersymmetric theory is constructed with a TeV sized extra dimension compactified on the orbifold S^1/(Z_2 \times Z_2'). The compactification breaks supersymmetry leaving a set of zero modes which correspond precisely to the states of the 1 Higgs doublet standard model. Supersymmetric Yukawa interactions are localized at orbifold fixed points. The top quark hypermultiplet radiatively triggers electroweak symmetry breaking, yielding a Higgs potential which is finite and exponentially insensitive to physics above the compactification scale. This potential depend…
