Unification through coset-space dimensional reduction

Surridge, Michael (1986) Unification through coset-space dimensional reduction. University of Southampton, Doctoral Thesis.

Abstract

The idea that nature may admit more than four spacetime dimensions was first proposed over sixty years ago. More recently, attempts to unify the fundamental forces by constructing unified Gauge Theories have met with some problems. It has become fashionable once again to hypothesise the existence of extra dimensions in order to construct alternative unification schemes. We review briefly both these areas of theoretical physics (Unified Gauge Theories and Dimensional Reduction). We then present a more detailed description of a class of dimensional reduction schemes in which the extra dimensions lie in a compact coset-space of Lie groups. We then reproduce a number of investigations carried out by the author into such schemes. In the process, a classification of all the possible ways in which such schemes can give rise to the observed gauge symmetries at electroweak energies or below is developed. Simple examples are described explicitly. Further to this, we investigate some features of the fermionic sector in such models. We deduce from two separate arguments (which nevertheless reflect similar underlying problems) that the isometry group of the compact spacetime factor must lie outside the gauge group in such a theory. Finally, we present a few examples where this is the case, highlighting the problems which have yet to be solved in an investigation of such theories. (D73138/87) eject

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