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Register a new userExistence and Stability of Non-Trivial Scalar Field Configurations in Orbifolded Extra Dimensions
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We consider the existence and stability of static configurations of a scalar field in a five dimensional spacetime in which the extra spatial dimension is compactified on an $S^1/Z_2$ orbifold. For a wide class of potentials with multiple minima there exist a finite number of such configurations, with total number depending on the size of the orbifold interval. However, a Sturm-Liouville stability analysis demonstrates that all such configurations with nodes in the interval are unstable. Nodeless static solutions, of which there may be more than one for a given potential, are far more interesting, and we present and prove a powerful general criterion that allows a simple determination of which of these nodeless solutions are stable. We demonstrate our general results by specializing to a number of specific examples, one of which may be analyzed entirely analytically.
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This paper provides a pedagogical introduction to the physics of extra dimensions focussing on the ADD, Randall-Sundrum and DGP models. In each of these models, the familiar particles and fields of the standard model are assumed to be confined to a four dimensional space-time called the brane; the brane is a slice through a higher dimensional space-time called the bulk. The geometry of the ADD, Randall-Sundrum and DGP space-times is described and the relation between Randall-Sundrum and Anti-de-Sitter space-time is explained. The necessary differential geometry background is introduced in an appendix that presumes no greater mathematical preparation than multivariable calculus. The ordinary wave equation and the Klein-Gordon equation are briefly reviewed followed by an analysis of the propagation of scalar waves in the bulk in all three extra-dimensional models. We also calculate the scalar field produced by a static point source located on the brane for all three models. For the ADD and Randall-Sundrum models at large distances the field looks like that of a point source in four space-time dimensions but at short distances it crosses over to a form appropriate to the higher dimensional space-time. For the DGP model the field has the higher dimensional form at long distances rather than short. The scalar field results provide qualitative insights into the corresponding behavior of gravitational fields. In particular the explanation within the ADD and Randall-Sundrum model of the weakness of gravity compared to other forces is discussed as are the implications of the two models for colliders and other experiments.
We analyze the behaviour of the high-energy scattering amplitude within the brane world scenario in extra dimensions. We argue that contrary to the popular opinion based on the Kaluza-Klein approach, the cross-section does not increase with energy, but changes the slope close to the compactification scale and then decreases like in the 4-dimensional theory. A particular example of the quark-antiquark scattering due to the gluon exchange in the bulk is considered.
Recently, a scenario has been proposed in which the gravitational scale could be as low as the TeV scale, and extra dimensions could be large and detectable at the electroweak scale. Although supersymmetry is not a requirement of this scenario, it is nevertheless true that its best-motivated realizations arise in supersymmetric theories (like M theory). We argue here that supersymmetry can have robust, and in some instances fatal, implications for the expected experimental signature for TeV-scale gravity. The signature of the supersymmetric version of the scenario differs most dramatically from what has been considered in the literature because mass splittings within the gravity supermultiplet in these models are extremely small, implying in particular the existence of a very light spin-one superpartner for the graviton. We compute the implications of this graviphoton, and show that it can acquire dimension-four couplings to ordinary matter which can strongly conflict with supernova bounds.
We propose gauge-Higgs unification in fuzzy extra dimensions as a possible solution to the Higgs naturalness problem. In our approach, the fuzzy extra dimensions are created spontaneously as a vacuum solution of certain four-dimensional gauge theory. As an example, we construct a model which has a fuzzy torus as its vacuum. The Higgs field in our model is associated with the Wilson loop wrapped on the fuzzy torus. We show that the quadratic divergence in the mass of the Higgs field in the one-loop effective potential is absent. We then argue based on symmetries that the quantum corrections to the Higgs mass is suppressed including all loop contributions. We also consider a realization on the worldvolume theory of D3-branes probing $C^3/(Z_N times Z_N)$ orbifold with discrete torsion.
Dynamical localization of non-Abelian gauge fields in non-compact flat $D$ dimensions is worked out. The localization takes place via a field-dependent gauge kinetic term when a field condenses in a finite region of spacetime. Such a situation typically arises in the presence of topological solitons. We construct four-dimensional low-energy effective Lagrangian up to the quadratic order in a universal manner applicable to any spacetime dimensions. We devise an extension of the $R_xi$ gauge to separate physical and unphysical modes clearly. Out of the D-dimensional non-Abelian gauge fields, the physical massless modes reside only in the four-dimensional components, whereas they are absent in the extra-dimensional components. The universality of non-Abelian gauge charges holds due to the unbroken four-dimensional gauge invariance. We illustrate our methods with models in $D=5$ (domain walls), in $D=6$ (vortices), and in $D=7$.
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