Effective potential for chiral scalar superfields

This paper contains two results. The first is that for a theory of N chiral scalar superfields, for which the supersymmetry is not spontaneously broken, the effective potential vanishes at the same points as the tree potential. This is also verified in the one- and two- loop approximation. It is concluded that the absolute minima of the tree potential are also absolute minima of the effective potential, and hence that any degeneracy in the tree potential will persist to all orders in the radiative corrections. The second result is that, in the case of one chiral superfield, the one-loop contribution to the effective potential not only vanishes at the zeros of the tree potential, but is non-negative at all other points. This result is taken as an indication that the supersymmetry itself is not spontaneously broken by the radiative corrections. (Auth.)