On the existence of the N-body Efimov effect

In this paper, we prove the existence of the Efimov effect for N-body quantum systems with N⩾4. Under the conditions that the bottom of the essential spectrum, E0, of the N-body operator is attained by the spectra of a unique three-cluster Subhamiltonian and its three associated two-cluster Subhamiltonians, and that at least two of these two-cluster Subhamiltonians have a resonance at the threshold E0, we give a lower bound of the form C0|log(E0−λ)| for the number of eigenvalues on the left of λ, λ