Physics in Higher Dimensions
Various open questions arising in four-dimensional particle physics have been studied within the higher-dimensional models such as Brane World models with infinite and warped extra dimensions as well as within the models with compact extra dimensions. Among the problems addressed are the hierarchy problem, supersymmetry breaking, dynamical electroweak symmetry breaking, the strong CP problem and the cosmological constant problem, grand unification and the quark-lepton compositeness.
In the framework of warped compactification proposed by Randall and Sundrum, we have investigated localization of gravity and the mass hierarchy problem in the presence of extra time-like dimension. While the proposed model allows one to reconcile the solution to the hierarchy problem with a correct cosmological expansion of the visible universe, it generally suffers from the appearance of phenomenologically dangerous tachyonic KK graviton modes. Some ways to overcome this problem have also been suggested. Particularly, we have constructed an intersecting brane configuration in six-dimensional space with one extra space-like and one extra time-like dimensions. With a certain additional symmetry imposed on the extra space-time we have found that effective four-dimensional cosmological constant vanishes automatically, providing the static solution with gravity fully localized at the four-dimensional intersection region as there are no propagating massive modes of graviton. In this way, the same symmetry allows us to eliminate tachyonic states of graviton from the spectrum of the effective four-dimensional theory, thus avoiding phenomenological difficulties coming from the matter instability usually induced in theories with extra time-like dimensions.
It has been pointed out that in a certain class of higher-dimensional theories such as Brane World models with quasi-localized non-Abelian gauge fields the vacuum structure turns out to be trivial. Since the gauge theory behaves at large distances as a 4+n-dimensional and thus the topology of the infinity is that of S3+n rather than S3, the set of gauge mappings are homotopically trivial and the CP-violating q-term vanishes on the brane world-volume. As well there are no contributions to the q-term from the higher-dimensional solitonic configurations. In this way, the strong CP problem is absent in the models with quasi-localized gluons.
The gauge hierarchy problem has been addressed within the models with compact extra dimensions as well. We have argued that the familiar gauge hierarchy between the fundamental Planck scale MPl and the electroweak scale MW, can be naturally explained in higher-dimensional theories with relatively large radii (Rc > 1/MPl) extra dimensions. In particular, we have shown that it is possible that the electroweak Higgs mass at high energies is of the order of MPl, but radiative corrections drive it to an infrared stable fixed-point ~MPl at low energies thus inducing a large hierarchy without any fine tuning of parameters.
Dynamical electroweak symmetry breaking through top condensation in the presence of compact large extra dimensions has been studied. It has been shown that owing to the power-low evolution of gauge and Yukawa couplings the original BHL predictions for the top quark mass are significantly lowered and even for small (of the order of TeV) cut-off scale one can obtain correct values for the top-quark mass.
We have considered supersymmetric models in 5-dimensional space-time compactified on S1/Z2 orbifold where N = 2 supersymmetry is explicitly broken down to N = 1 by the orbifold projection. We have found that the residual N = 1 supersymmetry is broken spontaneously by a stable classical wall-like field configurations which can appear even in the simple models discussed. We also consider some simple models of bulk fields interacting with those localized on the 4-dimensional boundary wall where N = 1 supersymmetry can survive in a rather non-trivial way.
A supersymmetric SU(5) model has been constructed in five-dimensions with S1/Z2 orbifold compactification. A salient feature of the model is that SU(5) symmetry breaking and doublet-triplet splitting are realized in an intrinsically geometric way through the orbifold projection. Moreover, placing matter in the five-dimensional bulk one automatically ensures the stability of the proton in all orders of perturbation theory and if so the unification scale can be lowered down to a TeV scale providing an interesting phenomenology for high energy colliders.
A new approach towards the composite structure of quarks and leptons in the context of the higher dimensional unified theories has been proposed. Owing to the QCD-like strong dynamics every possible vectorlike set of composites appears in higher dimensional bulk space-time, however, through a proper Sherk-Schwarz compactification only chiral multiplets of composite quarks and leptons survive as the massless states in four dimensions. Starting with the SU(5)-unified supersymmetric model of preons in 5D we come to just three generations of composite quarks and leptons being the triplets of the chiral horizontal symmetry SU(3)h which automatically appears in the composite spectrum when going to ordinary four dimensions.