Mirror Fermat Calabi-Yau Threefolds and Landau-Ginzburg Black Hole Attractors

Abstract

We study black hole attractor equations for one-(complex structure)modulus Calabi-Yau spaces which are the mirror dual of Fermat Calabi-Yau threefolds (CY_{3}s). When exploring non-degenerate solutions near the Landau-Ginzburg point of the moduli space of such 4-dimensional compactifications, we always find two species of extremal black hole attractors, depending on the choice of the Sp(4,Z) symplectic charge vector, one 1/2-BPS (which is always stable, according to general results of special Kahler geometry) and one non-BPS. The latter turns out to be stable (local minimum of the ``effective black hole potential'' V_{BH}) for non-vanishing central charge, whereas it is unstable (saddle point of V_{BH}) for the case of vanishing central charge. This is to be compared to the large volume limit of one-modulus CY_{3}-compactifications (of Type II A superstrings), in which the homogeneous symmetric special Kahler geometry based on cubic prepotential admits (beside the 1/2-BPS ones) only non-BPS extremal black hole attractors with non-vanishing central charge, which are always stable.