CERN-PH-TH/2006-154 UCLA/07/TEP/8 Mirror Fermat Calabi-Yau Threefolds and Landau-Ginzburg Black Hole Attractors Stefano Bellucci ♠ , Sergio Ferrara ♦,,♠ , Alessio Marrani ♥,♠ and Armen Yeranyan ♣,♠ ♠ INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40,00044 Frascati, Italy bellucci,marrani@lnf.infn.it ♦ Physics Department,Theory Unit, CERN, CH 1211, Geneva 23, Switzerland sergio.ferrara@cern.ch  Department of Physics and Astronomy, University of California, Los Angeles, CA USA ferrara@physics.ucla.edu ♥ Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi” Via Panisperna 89A, 00184 Roma, Italy ♣ Department of Physics, Yerevan State University, Alex Manoogian St., 1, Yerevan, 375025, Armenia ayeran@ysu.am 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 K¨ ahler 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 K¨ ahler 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. arXiv:hep-th/0608091v2 4 Apr 2007