Unified theories which are supersymmetric down to energies ∼${10}^3$-${10}^5$ GeV have been proposed as possible solutions to the gauge-hierarchy problem. The additional particles then required have significant effects on renormalization of coupling constants. The previous successful calculation of the weak mixing angle is only slightly changed, but the scale of unification is moved significantly higher, into the range of the Planck mass. This may be suggestive of an eventual unification including gravity, and markedly reduces the predicted rate of nucleon decay.

• Received 20 April 1981

DOI:https://doi.org/10.1103/PhysRevD.24.1681