Three Generations or More for an Attractive Gravity?

Abstract

We calculate the induced Einstein action from supersymmetric models in general space-time. Supersymmetric models consist of two kinds of supermultiplets, called scalar supermultiplets and vector supermultiplets, respectively. We show that the vector multiplets generate a negative Newton constant, while the scalar multiplets a positive one. Then we find that the positivity of Newton constant depends on the ratio of the number of scalar multiplets to one of vector multiplets. If we apply this result to two hopeful supersymmetric unified models: one is minimal SUSY standard model and another is minimal SUSY SU(5) GUT, we are led to the conclusion that we need more than or equal to three generations of quark and lepton multiplets to have a positive Newton constant, i.e., an attractive gravity.