\end{split}$$ which is written in terms of the affine coordinates $t^\alpha=z^\alpha/z^0$.

Having the form of the superpotential we need the form of the Kähler potential for the axio-dilaton and bulk moduli. This potential takes the form $$\eqlabel{ourkahler} K =-\log\left[ \ii (t_1-\bar t_1) (t_2-\bar
t_2)(t_3-\bar t_3) (\tau-\bar\tau)^4\right].$$ We need to pause to explain the structure of the Kähler potential for the axio-dilaton, $-4\log(\tau-\bar\tau)$ as opposed to the familiar $-\log(\tau-\bar\tau)$ (compare e.g. with the appendix of [@Giddings]). Recall that one way to define the model is to start on a large volume $T^6$, go to a symmetric point in Kähler moduli space and then orbifold in such a way as to project out all Kähler moduli (see Section \[model\]). Let us rephrase this in supergravity language, as this allows for an easier comparison with type IIA analysis of [@wati]. Assume that we have a four dimensional $\caln=2$ supergravity with some number $n_h$ of hypermultiplets, one of which is the universal hypermultiplet and some number $n_v$ of vector multiplets. In many cases, the moduli space of hypermultiplets contains a region in which the prepotential is cubic, and which can be derived by dimensional reduction from ten dimensional supergravity. Let us call it the 