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Higher-Dimensional Self-Consistent Solution With Deformed Internal Spaces, T. -C. Shen, J. Sobczyk

T. -C. Shen

We study a system of gravity and free massless scalar fields minimally coupled to gravity in a 7- dimensional background which is a direct product of a 4-dimensional Minkowski space and a 3- dimensional homogeneously deformed three-sphere. Compactification is caused by the vacuum energy of scalar fields. The effective potential as a function of two parameters (scale and deformation) is calculated numerically after dimensional regularization. We find the effective potential decreases rapidly toward negative infinity in both prolate and oblate directions. The classical curvature, however, can balance the quantum effect and yields three extrema. In addition to the round S …