Topological constraints on stabilized flux vacua

We study the influence of four-form fluxes on the stabilization of the Kähler moduli in M-theory compactified on a Calabi-Yau four-fold. We find that, under certain nondegeneracy condition on the flux, M5-instantons of a new topological type generate a superpotential. The existence of such an instanton restricts possible four-folds for which the stabilization by this mechanism is expected. These topological constraints on the background are different from the previously known constraints, derived from the flux-free analysis of the nonperturbative effects.