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We study the consequences of supersymmetry breaking in the computation of thenumber of solutions of the Thouless-Anderson-Palmer (TAP) equations. We showthat Kurchan argument that proves the vanishing of the prefactor of the Brayand Moore saddle point for the total number of solutions can be extended tosolutions at any given free energy. We also provide a new simple argument forthe vanishing of the prefactor and use it to prove that the isolated eigenvaluerecently considered by Aspelmeier, Bray and Moore is exactly zero in the BMtheory because of supersymmetry breaking. The behavior of the eigenvector ofthe isolated eigenvalue at the lower band edge is also considered.Comment: 12 page

On supersymmetry breaking in the computation of the complexity