Supersymmetric multiple basin attractors

We explain that supersymmetric attractors in general have several criticalpoints due to the algebraic nature of the stabilization equations. We show thatthe critical values of the cosmological constant of the adS_5 vacua are givenby the topological (moduli independent) formulae analogous to the entropy ofthe d=5 supersymmetric black holes. We present conditions under which more thanone critical point is available (for black hole entropy as well as to thecosmological constant) so that the system tends to its own locally stableattractor point. We have found several families of Z_2-symmetric criticalpoints where the central charge has equal absolute values but opposite signs intwo attractor points. We present examples of interpolating solutions anddiscuss their generic features.Comment: 14 pages, 1 fig, JHEP, added proof of positivity of vector metric at critical points, analysis of interpolating solutions, and ref