Kaluza-Klein theories

Abstract

Kaluza-Klein theory is developed starting from the simplest example in which a single extra spatial dimension is compactified to a circle, and a single Abelian gauge field emerges in four dimensions from the higher-dimensional metric. This is generalised to greater dimensionality whence non-Abelian gauge groups may be obtained, and possible mechanisms for achieving the compactification of the extra spatial dimensions are discussed. The spectrum of particles appearing in four dimensions is discussed with particular emphasis on the spectrum of light fermions, and the constraints arising from cancellation of anomalies when explicit higher-dimensional gauge fields are present are studied. Cosmological aspects of these theories are described, including possible mechanisms for cosmological inflation, and relic heavy particles. Finally, an introductory account of Kaluza-Klein supergravity is given leading towards superstring theory.