The hierarchy problem and new dimensions at a millimeter

We propose a new framework for solving the hierarchy problem which does not rely on either supersymmetry or technicolor. In this framework, the gravitational and gauge interactions become united at the weak scale, which we take as the only fundamental short distance scale in nature. The observed weakness of gravity on distances greater than or similar to 1 mm is due to the existence of n greater than or equal to 2 new compact spatial dimensions large compared to the weak scale. The Planck scale M-Pl similar to G(N)(-1/2) is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely propagate in the new dimensions, at sub-weak energies the Standard Model (SM) fields must be localized to a 4-dimensional manifold of weak scale "thickness" in the extra dimensions. This picture leads to a number of striking signals for accelerator and laboratory experiments. For the case of n = 2 new dimensions, planned sub-millimeter measurements of gravity may observe the transition from 1/r(2) --> 1/r(4) Newtonian gravitation. For any number of new dimensions, the LHC and NLC could observe strong quantum gravitational interactions. Furthermore, SM particles can be kicked off our 4 dimensional manifold into the new dimensions, carrying away energy, and leading to an abrupt decrease in events with high transverse momentum p(T) greater than or similar to TeV. For certain compact manifolds, such particles will keep circling in the extra dimensions, periodically returning, colliding with and depositing energy to our four dimensional vacuum with frequencies of similar to 10(12) Hz or larger. As a concrete illustration, we construct a model with SM fields localized on the 4-dimensional throat of a vortex in 6 dimensions, with a Pati-Salam gauge symmetry SU(4) X SU(2) X SU(2) in the bulk. (C) 1998 Published by Elsevier Science B.V. All rights reserved.