A topological formula for the Kaehler potential of a 4D N=1, 2 strings, and its implications for the moduli problem

Using recently established results on the superconformal moduli space and their relation to the geometry of N=2 SUGRA, we given an explicit formula for the Kaehler potential for the chiral multiplets associated to deformation of the Kaehler class [(1, 1) forms]. The formula holds for all compactifications on (2, 2) systems and it requires only topological informations about the internal superconformal theory (i.e. the intersection numbers). The metric turns out to be the unique Kaehler metric which is conformal to the one proposed by Strominger some time ago. From this fact we infer that the cone in H2(K, R) consisting of Kaehler classes coincides with a class of convex cones whose remarkable geometrical properties were already noticed in the contexts of N=2 supergravity and Jordan algebras. Our formula gives a closed expression for this Kaehler cone. (orig.)