Abstract
We obtain an expression for the one loop effective potential coming from quantum fluctuations of scalars and spin-1/2 fermions in a higher-dimensional manifold of product form M/sup 4/ x S/sup M/ x S/sup N/. In contrast to previous calculations, we consider the case in which the total number of dimensions is even, since this is the relevant case for superstring compactification. A detailed calculation for a ten-dimensional spacetime with two internal 3-spheres is performed, and an approximate static solution for the geometry is found, with the two internal radii being of the order of the Planck length for a sufficiently large number of matter fields. We study the stability of this solution and make some remarks on the possible cosmological implications of our results.
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