Locally Supersymmetric Grand Unification

Abstract

A locally supersymmetric grand unification program is proposed which couples the $N=1$ supergravity multiplet to an arbitrary grand unified gauge group with any number of left-handed chiral multiplets and a gauge vector multiplet. A specific model is discussed where it is shown that not only do the gravitational interactions eliminate the degeneracy of the vacuum state encountered in global supersymmetry, but simultaneously they can break both supersymmetry and SU(2) \ensuremath{\bigotimes} U(1) down to a residual $\mathrm{SU}{(3)}^{c}\ensuremath{\bigotimes}\mathrm{U}(1)$ symmetry at \ensuremath{\sim}300 GeV.