Stability and supersymmetry: General formalism and explicit two-loop applications

A complete account of a perturbative investigation of ground state instability is presented for a massless theory involving scalar, pseudoscalar, and Majorana spinor fields. The effective potential, dimensional regularization, and renormalization group formalisms are briefly reviewed and then applied in detail to show the semiclassical vacuum of the model is unstable due to radiative corrections when the (pseudo)scalar self-interaction strength, f, is less than the fermion-(pseudo)scalar coupling, g². Models with stable ground states are found when f ≤ g², and when f = g² a supersymmetric theory is obtained. The supersymmetric case is thus encountered as a boundary between stable and unstable models. This results is discussed and is conjectured to be a general feature of supersymmetric theories. All perturbative calculations in the analysis are methodically carried out to the level of two-loop Feynman diagrams, and to this level, a variety of renormalization prescriptions are considered. The correlation of the various ultraviolet divergences for the supersymmetric model is explicitly demonstrated and shown not to hold in the general theory.