ON QUANTUM SPECIAL KAHLER GEOMETRY

We compute the effective black hole potential V-BH of the most general N = 2, d = 4 (local) special Kahler geometry with quantum perturbative corrections, consistent with axion-shift Peccei-Quinn symmetry and with cubic leading order behavior. We determine the charge configurations supporting axion-free attractors, and explain the differences among various configurations in relations to the presence of flat directions of V-BH at its critical points. Furthermore, we elucidate the role of the sectional curvature at the nonsupersymmetric critical points of V-BH, and compute the Riemann tensor (and related quantities), as well as the so-called E-tensor. The latter expresses the nonsymmetricity of the considered quantum perturbative special Kahler geometry.