Induced Gravity in Higher-Dimensional Spacetime and the Mass Scale of the Kaluza-Klein Theory

Abstract

that the mass structure of the fundamental particles which couple to gauge fields may be understood in relation with the above mechanism of the dimensional reduction. In the usual dimensional reduction, however, the mass scale arising from the extra space is restricted to the order of the Planck mass because of the constraint e 2 x 2 = 16J[C, where x, e and C represent the size of the extra space, gauge coupling constant, and Newton's gravitational constant respectively. The appearance of the constraint is due to the fact that the action of the gauge fields is derived from the Einstein action in the higher­ dimensional spacetime, in which only the gravitational constant plays the role of a dimensional constant. In order to avoid the problem of the Planck mass, several attempts have been made, for example, by extending the Einstein action in the higher-dimensional spacetime. 4 ) The purpose of the present paper is to investigate a method for avoiding the problem of Planck mass from the viewpoint of the induced gravity.5) In that theory, the metric tensor of spacetime is obtained as a quantum fluctuation of fundamental matter fields and the effective action is defined with a suitable cutoff parameter for the ultraviolet divergence coming from the loop calculations in each spacetime dimension. Then we can expect that if we use dijferent cutoff parameters between the four-dimensional spacetime and the extra space, it will be possible to introduce a dimensional constant other than x and C into the theory.