On space-time compactification induced by a general non-linear sigma model

Abstract

A compactification scheme for the Kaluza-Klein theory in six dimensions is attempted using a general non-linear σ-model. The general lagrangian for the σ-model consists of a leading term and a higher derivative term in the scalar field φ. With scalar fields on G/H, the above scheme is shown to give compactification with a minkowskian flat M 4, and a compact two-dimensional manifold whose metric is proportional to the scalar manifold metric. The Kaluza-Klein vector bosons are shown to remain massless. The formal equivalence of this scheme with the monopole-induced compactification is discussed.