Generic approach to dimensional reduction and selection principle for low-energy limit of M theory

Abstract

We propose the approach to deriving lower-dimensional limit of modern high-energy theory which does not make explicit use of the Kaluza-Klein scheme and predefined compactification manifolds. The approach is based on the selection principle in which a crucial role is played by p-brane solutions and their preservation, in a certain sense, under dimensional reduction. Then we engage a previously developed method of reconstruction of a theory from a given solution which eventually leads to some model acting in the space of field couplings. Thus, our approach focuses on those general features of effective 4D theories which are independent of how the decomposition of spacetime dimensions into ``observable'' and ``unobservable'' ones could be done. As an example, we exactly derive the simplified abelian sector of the effective low-energy M-theory together with its fundamental 0-brane solution describing the family of charged black holes with scalar hair in asymptotically flat, de Sitter or anti-de Sitter spacetime.