the non-harmonic part $V$ included in the Kähler potential for $S$.

\[sub:d\_SWne0\]$\partial_{S}W\ne0$
-----------------------------------

The discussion in the previous subsection remains valid if the superpotential dependence on $S$ is no more than linear. This is the case for instance in type IIB string theory, provided the pre-factors of the non-perturbative terms responsible for breaking the no-scale structure and stabilizing the Kaehler moduli are independent of $S$ (or at least no more than linear in $S$). Thus under these usual assumptions one has $$W=A(\phi)+B(\phi)S,\label{eq:WIIB}$$ where as in the last subsection $\phi$ stands for all the other chiral scalar superfields. In this case the only relevant change is in equation (\[eq:deltaS\]), which is replaced by $$-3(-\frac{1}{4}\bar{\nabla}^{2}+2R)(Ue^{-K/3})+\frac{k}{4}{\cal W}^{2}+B(\phi)=0.$$ Equation will remain the same with $W\rightarrow A(\phi)$ but on evaluating the components of the first term we would need to replace $k{\cal W}^{2}\rightarrow k{\cal W}^{2}+B(\phi)$. The main results of the previous subsection remain unchanged.

However when the superpotential is non-linearly dependent on $S$ these results cannot be obtained. The reason is that the $\delta S$ equation no longer gives a constraint on the unconstrained superfield $U$. Instead it becomes an equation which expresses the chiral superfield S in terms of a chiral projection of an 