Simple argument for unexpected behavior in SUSY model

Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential $$W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ One can show, by doing calculations, that (i) supersymmetry is spontaneously broken, but (ii) one-loop corrections do not lift the classical pseudo-moduli space.

QUESTION: is it possible to say (ii) without looking at the explicit form of Coleman-Weinberg potential, e.g. making some field redefinition which shows that this is not an interacting theory and it is very close to Polonyi model?

• Yay, a good question after so many days! I hope you get an answer... – Abhimanyu Pallavi Sudhir Sep 4 '13 at 12:44
• This does not seem obvious .Following this paper, it we take a model similar to yours, but different, the O’Raifeartaigh model $(7.32)$, one may show that quantum corrections lift the classical pseudo-moduli space, see Chapter $7.4$ and formula $7.51$. – Trimok Sep 4 '13 at 17:09
• right, but this is not the O'Raifeartaigh model – jj_p Sep 5 '13 at 8:06
• @Nicolo': Comparing your calculus, with the calculus done for O’Raifeartaigh model, maybe you can check the step, or the steps, where the difference happens. Maybe this will give an idea for some possible "rule". – Trimok Sep 5 '13 at 9:37