Gauge Hierarchy from $Ad{S}_5$ Universe with 3-Branes

Abstract

If the universe is (or a slice of) $Ad{S}_5$ space with 3-branes, the 5-dimensional GUT scale on each brane can be indetified as the 5-dimensional Planck scale, but, the 4-dimensional Planck scale is generated from the low 4-dimensional GUT scale exponentially in our world. The 4-dimensional GUT scales and Planck scale are related to the 5-dimensional GUT scales and Planck scale by exponential factors, respectively. One of such scenarios was suggested by Randall and Sundrum recently. We give another scenario that the 4-dimensional Planck scale is generated from the low five-dimensional Planck scale by an exponential hierarchy, and the mass scale in the Standard Model is not rescaled from the 5-dimensional metric to the 4-dimensional metric. We also argue that the additional constant in the solution might exist, which will rescale the 5-dimensional Planck scale and affect the physical scale picture. Finally, we embed those compactifications to the general compactification on $Ad{S}_5$ space and discuss the origin of the additional constant.

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