Narrow Results

In this paper, we review the calculations that are needed to obtain the bosonic and fermionic effective potential at finite temperature and volume (at one loop). The calculations at finite volume correspond to S¹ × R^d topology. These calculations appear in the calculation of the Casimir energy and of the effective potential of extra dimensional theories. In the case of finite volume corrections, we impose twisted boundary conditions and obtain semi-analytic results. We mainly focus in the details and validity of the results. The zeta function regularization method is used to regularize the infinite summations. Also the dimensional regularization method is used in order to renormalize the UV singularities of the integrations over momentum space. The approximations and expansions are carried out within the perturbative limits. After the end of each section, we briefly present applications associated to the calculations. Particularly the calculation of the effective potential at finite temperature for the standard model fields, the effective potential for warped and large extra dimensions, and the topological mass creation. In the end, we discuss on the convergence and validity of one of the obtained semi-analytic results.

We discuss some issues arising in studying (linearized) gravity on non-BPS higher co-dimension branes in an infinite-volume bulk. In particular, such backgrounds are badly singular for codimension-3 and higher δ-function-like branes with nonzero tension. As we discuss in this note, nontrivial issues arise in smoothing out such singularities. Thus, adding higher curvature terms might be necessary in this context.

We discuss the decoupling solution to SUSY flavor problem in the fat brane scenario. We present a simple model to yield the decoupling sfermion spectrum in a five-dimensional theory. Sfermion masses are generated by the overlap between the wave functions of the matter fields and the chiral superfields on the SUSY breaking brane. Two explicit examples of the spectrum are given.

In models with flat extra dimensions tiny Dirac neutrino masses can be generated via the coupling of four-dimensional Standard Model fields to a higher dimensional fermion. Here we argue that, in spite of the Dirac nature of the neutrino, quantization of the electric charge can still be understood as a result of anomaly cancellation, charge conservation and naturalness requirements.

We propose a method to extend to the bulk asymptotically flat static spherically symmetric brane-world metrics. We employ the multipole (1/r) expansion in order to allow the exact integration of the relevant equations along the (fifth) extra coordinate and make contact with the parametrized post-Newtonian formalism. We apply our method to three families of solutions previously appeared as candidates of black holes in the brane world and show that the shape of the horizon is very likely a flat "pancake" for astrophysical sources.

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of most brane cosmological models is that the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we re-examine the classification of the second-order symmetric tensors in 5-D, and prove two theorems which collect together some basic results on the algebraic structure of these tensors in five-dimensional spacetimes. We also briefly indicate how one can obtain, by induction, the classification of symmetric two-tensors (and the corresponding canonical forms) on n-dimensional (n>4) spaces from the classification on four-dimensional spaces. This is important in the context of 11-D supergravity and 10-D superstrings.

We calculate the linearized metric perturbations in the five-dimensional two-brane model of Randall and Sundrum. In a carefully chosen gauge, we write down and decouple Einstein equations for the perturbations and get the final and simple perturbative metric ansatz. This ansatz turns out to be equal to the linear expansion of the metric solution of Charmousis et al.¹ We show that this ansatz, the metric ansatz of Boos et al.² and the one of Das and Mitov³ are not incompatible, as it appears on the surface, but completely equivalent by an allowed gauge transformation that we give.

We emphasize that the group-theoretical considerations leading to SO(10) unification of electroweak and strong matter field components naturally extend to spacetime components, providing a truly unified description of all generation degrees of freedoms in terms of a single chiral spin representation of one of the groups SO(13,1), SO(9,5), SO(7,7) or SO(3,11). The realization of these groups as higher-dimensional spacetime symmetries produces unification of all fundamental fermions is a single spacetime spinor.

We discuss the Schwarzschild solution in the Dvali–Gabadadze–Porrati (DGP) model. We obtain a perturbative expansion and find the explicit form of the lowest-order contribution. By keeping off-diagonal terms in the metric, we arrive at a perturbative expansion which is valid both far from and near the Schwarzschild radius. We calculate the lowest-order contribution explicitly and obtain the form of the metric both on the brane and in the bulk. As we approach the Schwarzschild radius, the perturbative expansion yields the standard four-dimensional Schwarzschild solution on the brane which is non-singular in the decoupling limit. This non-singular behavior is similar to the Vainshtein solution in massive gravity demonstrating the absence of the van Dam–Veltman–Zakharov (vDVZ) discontinuity in the DGP model.

Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must appear. Little is known about the fundamental theory valid at Planckian energies, except that it necessarily seems to imply the occurrence of a minimal length scale, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime.

Motivated by String Theory, the models of large extra dimensions lower the Planck scale to values soon accessible. These models predict a vast number of quantum gravity effects at the lowered Planck scale, among them the production of TeV-mass black holes and gravitons. Within the extra dimensional scenario, the minimal length also comes into the reach of experiment and sets a fundamental limit to short distance physics.

We review the status of Planck scale physics in these effective models.

We present a class of models of flavor that rely on the use of flavor symmetries and the Froggart–Nielsen mechanism in extra dimensions. The particle content is that of the standard model plus an additional flavon field; all the fields propagate in universal extra dimensions and the flavor scale is associated with the cutoff of the theory, which in 5D is ~ 10 TeV. The Yukawa matrices are generated by higher dimension operators involving flavon fields, whose vacuum expectation values break the flavor symmetry. We apply this framework and present a specific 5D model based on a discrete local symmetry that reproduces all fermion masses and mixing angles both in the quark and charged lepton sectors.

We investigate coupled gravity and a bulk scalar field on a slice of AdS₅ bulk with special BPS branes at the two ends. With a careful treatment of the general coordinate invariance, the complete tensor–scalar spectrum is presented. There are two massless zero modes in the scalar sector, the radion and a dilatonic zero mode. The four-dimensional effective action is of biscalar–tensor type.

We study , i = e, μ, τ decays in the two-Higgs doublet model, with the inclusion of one and two spatial non-universal extra dimensions. We observe that the branching ratio is sensitive to two extra dimensions in contrary to a single extra dimension.

We study a gravity model where a tensionful codimension-one three-brane is embedded in a bulk with infinite transverse length. We find that 4D gravity is induced on the brane already at the classical level if we include higher-curvature (Gauss–Bonnet) terms in the bulk. Consistency conditions appear to require a negative brane tension as well as a negative coupling for the higher-curvature terms.

In this work we deal with the extension of the Kaluza–Klein approach to a non-Abelian gauge theory; we show how we need to consider the link between the n-dimensional model and a four-dimensional observer physics, in order to reproduce field equations and gauge transformations in the four-dimensional picture. More precisely, in field equations any dependence on extra coordinates is canceled out by an integration, as consequence of the unobservability of extra dimensions. Thus, by virtue of this extra dimension unobservability, we are able to recast the multidimensional Einstein equations into the four-dimensional Einstein–Yang–Mills ones, as well as all the right gauge transformations of fields are induced. The same analysis is performed for the Dirac equation describing the dynamics of the matter fields and, again, the gauge coupling with Yang–Mills fields are inferred from the multidimensional free fields theory, together with the proper spinors transformations.

We review electroweak symmetry breaking in supersymmetric models with a compact fifth dimension, the interval. We show how boundary conditions for hypermultiplets can be obtained dynamically by brane mass terms, and present formulas for the spectrum in the presence of general bulk mass matrices. After giving a brief overview on the literature of models, we describe in detail a recently proposed model that at energies below the compactification scale reduces to the MSSM with a very peculiar superpartner spectrum.

Considering that gravitational force might deviate from Newton's inverse-square law and become much stronger in small scale, we present a method to detect the possible existence of extra dimensions in the ADD model. By making use of an effective variational wave function, we obtain the nonrelativistic ground energy of a helium atom and its isoelectronic sequence. Based on these results, we calculate gravity correction of the ADD model. Our calculation may provide a rough estimation about the magnitude of the corresponding frequencies which could be measured in later experiments.

While the importance of phase space constraints for gravitational clustering of neutrinos (which are fermions) is well recognized, the explicit use of such constraints to limit neutrino emission from ultra energetic sources has not been stressed. Special and general relativistic phase space constraints are shown to limit neutrino luminosities in compact sources in various situations.

We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the presence of dark matter, is the result of the dynamical evolution of particles in higher dimensional spacetimes. Hence, dark matter may be a direct consequence of the presence of an extra force, generated by the presence of extra dimensions, which modifies the dynamic law of motion, but does not change the intrinsic properties of the particles, like, for example, the mass (inertia). We discuss in some detail several possible particular forms for the extra force, and the acceleration law of the particles is derived. Therefore, the constancy of the galactic rotation curves may be considered as an empirical evidence for the existence of the extra dimensions.

Experiments will soon start taking data at CERN's Large Hadron Collider (LHC) with high expectations for discovery of new physics phenomena. Indeed, the LHC's unprecedented center-of-mass energy will allow the experiments to probe an energy regime where the standard model is known to break down. Here, the experiments' capability to observe new resonances in various channels is reviewed.