Aspects of Kaluza-Klein Theories

The review part of thesis contains detailed discussions of five-dimensional Kaluza-Klein theory (KKT), zero-mode ansatz and six-dimensional model due to Randjbar-Daemi, Salam & Strathdee as well as basic information about different compactification mechanisms, stability problem, treatment of fermions in KKT harmonic expansion on homogeneous spaces, chiral anomalies and model proposed by Candelas & Weinberg. Original contributions are devoted to different aspects of KKT. Compactification of D=lO dimansional SU(3)xU(l) Einstein-Yang-Mills (EYM) theory to M4xCP(3) is shown to be classically stable. The gauge symmetry seen in four dimensions is SU(4)xU(l), first being the isometry of CP(3) and second - an unbroken part of initial gauge group. The topologically nontrivial background configuration of SU(3)x U(1) gauge fields makes it possible to obtain massless chiral fermions in four dimensions after compactification. Asymmetry in left and right handed zero modes agrees with that predicted by the Atiyah & Singer theorem. A relation between spontaneous compactification mechanism and chiral anomalies is investigated. A simple model (SU(3) EYM theory in D=6 dimensions with M4xs2 background geometry) is used to argue that the theory is free from chiral anomalies in higher dimensions if and only if the effective theory of zero modes in four dimensions is also anomaly-free. Correspondence between different types of gauge and gravitational (and mix) anomalies in D=6 and D=4 dimensions is displayed. Two possibilities of getting a natural symmetry breaking mechanism in KKT are investigated. In the framework of KKT with elementary gauge fields in higher dimensions, it is shown that one can obtain a solution of classical field equations with infinitesimally deformed N-sphere as the internal manifold, if a multiplet of scalar fields is added to the theory. In the D=6 dimensional model the symmetry breaking pattern 0(3)xU(1) --> 0(2) (a subgroup of 0(3)) results. Masses of initially massless (as deformation vanishes) vector gauge bosons are calculated. They are of order £ /a, where £ is a deformation parameter, and a is a Planck's length. The deformed background configuration can be made classically stable. In the context of the model due to Candelas & Weinberg, a total effective potential for a D=7 dimensional case with massless scalar fields minimally coupled to gravity is calculated. The background configuration is taken to be M4x3S3, S3 being a homogeneously deformed three-sphere with isometry 8U(2)xU(l). The effective potential as a function of two parameters (scale of S3 and deformation) has a local minimum for a non-zero deformation. The round S3 corresponds to a local maximum of the potential. Therefore the dynamics itself (quantum fluctuations of scalar fields) can determine the actual shape of the internal manifold.