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 ${\mathrm{AdS}}_5$ vacua in M theory compactified on positive Kähler-Einstein spaces, providing further evidence for the recent conjecture that any nonsupersymmetric anti–de Sitter vacuum supported by fluxes must be unstable.

Figure 1

Numerical solution to Eq. (26).

Figure 2

The graphs of $\alpha (r)$ and its derivative. The horizontal axes are $r-r_0$. The values of $f_0$ from top to bottom are 0.63, 0.62, 0.61 respectively.