In the supersymmetric case, such a small coupling for quartic interaction cannot be realized if the potential is lifted by the gauge D-term interactions, since, if so, the coupling constant λ becomes of the order O(g2) where g is the gauge coupling constant in the standard model. Therefore, we focus our attention on the D-flat directions. For D-flat directions, we have to be more careful since behaviors of the potential depend on which flat direction we consider. In the MSSM, Yukawa interactions exist in the superpotential to generate the fermion masses. Such Yukawa interactions lift some of the D-flat directions. In addition, we can also find several D-flat directions which are not affected by the Yukawa interactions associated with the fermion masses; without R-parity violation, such D-flat directions are only lifted by the effects of supersymmetry breaking.33Here, we assume that coefficients of non-renormalizable terms are suppressed enough to be neglected. This may be explained by the R-symmetry, assigning R-charge 23 to each MSSM chiral superfields. (See Ref. [6] for the details.)
