Multidimensional Einstein-Yang-Mills theories: Dimensional reduction, spontaneous compactification, and all that

We study some new aspects of dimensional reduction and spontaneous compactification in multidimensional Einstein-Yang-Mills theories. Relations between physical properties (spontaneous symmetry breaking, absence of ghosts and tachyons) of the reduced theory and the metric on the multidimensional space and its symmetries are established. Assuming the space of extra dimensions to be a generic coset space we find an effective potential for the spontaneous compactification equations and investigate a class of models possessing compactifying solutions with remarkable properties: (a) the multidimensional vacuum states correspond to the phase with spontaneous symmetry breaking of the reduced theory, (b) there exist solutions with compact time-like extra-dimensions, (c) one of the solutions leads to enlargement of the initial symmetry group of the metric of the internal space. (orig.)