New Kaluza-Klein instantons and the decay of AdS vacua

We construct a generalization of Witten's Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten's instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We use the solution to exhibit the instability of nonsupersymmetric AdS(5) vacua in M theory compactified on positive Kahler-Einstein spaces, providing further evidence for the recent conjecture that any nonsupersymmetric anti-de Sitter vacuum supported by fluxes must be unstable.