Non perturbative instabilities of Anti-de Sitter solutions to M-theory

Ooguri and Vafa have recently conjectured that in a consistent theory of quantum gravity, all non supersymmetric Anti-de Sitter solutions supported by fluxes must be unstable. Whenever the solution is perturbatively stable, it is interesting to investigate possible non perturbative mechanisms leading to instabilities. A prototypical such mechanism is provided by Witten’s bubble of nothing, which demonstrates the instability of the Kaluza-Klein vacuum. The thesis aims at testing further the Ooguri-Vafa conjecture by studying generalizations of Witten's solution in the context of M-theory compactifications.