The Universe as a Topological Defect in a Higher-Dimensional Einstein-Yang-Mills Theory

An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein-Yang-Mills (EYM) theory. We start with $D$-dimensional EYM theory in our present analysis. A compactification leads to a $D-2$ dimensional effective action of Abelian gauge-Higgs theory. We find a "vortex" solution in the effective theory. Our universe appears to be confined in a center of a "vortex", which has $D-4$ large dimensions. In this paper we show an example with $SU(2)$ symmetry in the original EYM theory, and the resulting solution is found to be equivalent to the "instanton-induced compactification". The cosmological implication is also mentioned.