A classical model of Kaluza-Klein theories with torsion

Recent attempts in which torsion in the extra dimensions of a multidimensional unified theory is seen as a compactifying agent introduce spin condensates with no energy-momentum counterpart. While this is legitimate from the quantum viewpoint, it has no classical limit. We work out a Kaluza-Klein multidimensional extention of an Einstein-Cartan theory with a totally antisymmetric torsion on the spacetime as well as on the internal dimensions, providing a classical background in which more general compactification mechanisms could be analysed. The dimensional reduction of the field equation gives an Einstein-Cartan-Yang-Mills theory. A sufficient condition for the dimensional reduction of a multidimensional model in the presence of torsion is specified