Quantum lift of non-BPS flat directions

We study N = 2, d = 4 attractor equations for the quantum corrected two-moduli prepotential F = st(2) + i lambda, with lambda real, which is the only correction which preserves the axion shift symmetry and modifies the geometry. In the classical case the black hole effective potential is known to have a flat direction. We found that in the presence of D0-D6 branes the black hole potential exhibits a flat direction in the quantum case as well. It corresponds to non-BPS Z not equal 0 solutions to the attractor equations. Unlike the classical case, the solutions acquire non-zero values of the axion field. For the cases of D0-D4 and D2-D6 branes the classical flat direction reduces to separate critical points which turn Out to have a vanishing axion field. (C) 2008 Published by Elsevier B.V.