ABSTRACT

This chapter discusses the effective action in multidimensional gravity and supergravity on a compactified background. It considers the calculation of the EA on a com-pactified background where non-diagonal elements are equal to zero in the parametrization. The chapter shows the possibility of explicit calculation of two-loop effective action in multidimensional Einstein gravity on a torus compactified background. The contribution of matter fields to the quantum EA on the multidimensional compactified background has been calculated by many authors. The natural question is connected with the possibility of extending our consideration beyond the one-loop approximation. It is well-known that the investigation of the effective action in quantum gravity beyond the one-loop approximation is quite complicated. The appearence of winding numbers is a new phenomenon in comparison with Kaluza-Klein theories.