Effects of Extra Space-time Dimensions on the Fermi Constant

Effects of Kaluza-Klein excitations associated with extra dimensions with large radius compactifications on the Fermi constant are explored. It is shown that the current precision determinations of the Fermi constant, of the fine structure constant, and of the W and Z mass put stringent constraints on the compactification radius. The analysis excludes one extra space time dimension below $\sim 1.6$ TeV, and excludes 2, 3 and 4 extra space dimensions opening simultaneously below $\sim$ 3.5 TeV, 5.7 TeV and 7.8 TeV at the $90% CL$. Implications of these results for future collider experiments are discussed.