Extra Dimensions

For explanation of terms used and discussion of significant model dependence of following limits, see the " Extra Dimensions Review. " Limits are expressed in conventions of of Giudice, Rattazzi, and Wells as explained in the Review. Footnotes describe originally quoted limit. n indicates the number of extra dimensions. Limits not encoded here are summarized in the " Extra Dimensions Review. " The large separation between the weak scale ∼ 10 3 GeV and the traditional scale of gravity—the Planck scale with M Pl ∼ 10 19 GeV—is one of the most puzzling aspects of nature. The origin of this large ratio, as well as its stability under radiative corrections, demands explanation. This is known as the hierarchy problem. One theoretical means of solving this problem is to introduce Supersymmetry (see the " Note on Su-persymmetry " in this Review). Alternatively one may hope to address the hierarchy by exploiting the geometry of space time. Specifically, recent theories involve the idea that the 3-spatial dimensions in which we live could be a 3-spatial-dimensional 'membrane' embedded in a much larger extra dimensional space, and that the hierarchy is generated by the geometry of the additional dimensions. Such ideas have led to extra dimensional theories which have verifiable consequences at the TeV scale. Our knowledge of the weak and strong forces extends down to scales of ∼ (100 GeV) −1 (or of order 10 −15 mm). On the other hand, we have almost no knowledge of gravity at distances less than roughly a millimeter, as direct tests of the gravitational force at the smallest distances are based on