We study N=2, d=4 attractor equations for the quantum corrected two-moduli prepotential $mathcal{F}=st^2+ilambda$, with $lambda$ real, which is the only correction which preserves the axion shift symmetry and modifies the geometry. In the classical c
ase 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 $Z eq 0$ 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.
The motion of a particle near the Reissner-Nordstrom black hole horizon is described by conformal mechanics. In this paper we present an extended one-dimensional analysis of the N=4 superconformal mechanics coupled to n copies of N=8, d=1 vector supe
rmultiplets. The constructed system possesses a special Kahler geometry in the scalar sector of the vector multiplets as well as an N=4 superconformal symmetry which is provided by a proper coupling to a dilaton superfield. The superconformal symmetry completely fixes the resulting action. We explicitly demonstrate that the electric and magnetic charges, presenting in the effective black hole action, appear as a result of resolving constraints on the auxiliary components of the vector supermultiplets. We present the component action, supercharges and Hamiltonian with all fermionic terms included. One of the possible ways to generalize the black hole potential is to consider a modified version of the N=4 superconformal multiplet where its auxiliary components acquire non-zero constant values. We explicitly write down the corresponding modified black hole potential.
