Supersymmetric Multiple Basin Attractors

We explain that supersymmetric attractors in general have several critical points due to the algebraic nature of the stabilization equations. We show that the critical values of the cosmological constant of the adS5 vacua are given by the topological (moduli-independent) formulae analogous to the entropy of the d = 5 supersymmetric black holes. In one-moduli case critical points with positive definite metric and gauge couplings exist under condition that the central charge changes the sign from one critical point to the other. We have found several families of Z2-symmetric critical points where the central charge has equal absolute values but opposite signs in two attractor points. We present examples of interpolating solutions and discuss their generic features.