On the origin of compactification in the superstring theory

Abstract

The D -dimensional superstring theory is considered in the anisotropic space-time d s 2 = d t 2 −exp[2α( t )]d x 2 − exp[2β( t )]d y 2 , where exp[α( t )] is the radius function of the M -dimensional physical space, whose curvature is K , exp[β( t )] is the radius function of the N -dimensional internal space, whose curvature is , and D = M + N + 1. To lowest order in the slope parameter α′, the classical equations of motion are known to admit the solution α= −β, when K =0, provided that ( M−N) 2 = M+N , a condition which includes most cases of physical interest. Here it is pointed out, applying recent results and conjectures in superstring theory, that this solution may be dual to the isotropic solution α = β. This suggests that the anisotropic solution is favoured as the consequence of a symmetry-breaking process, which yields some understanding of how the compactification mechanism occurs, and of why the Universe does not expand in a completely isotropic fashion.