Bubbles of nothing and AdS instabilities

In this contribution we review the ideas and results presented in the articles [1] and [2] where the decay of AdS vacua into bubbles of nothing is studied. We firstly consider AdS vacua in General Relativity with a cosmological constant and in arbitrary dimensions. In this context we study a class of gravitational instantons generalizing the Witten's bubble of nothing and we discuss the derivation of the euclidean action. Secondly we consider a “stringy” non-supersymmetric AdS₄ vacuum arising in a compactification of massive IIA supergravity on a S⁶ and preserving G₂ symmetry. This vacuum has been shown to have a fully stable KK spectrum and also to be protected against brane-jet decays. In this framework we discuss a bubble solution in massive IIA connected to the G₂-invariant vacuum and associated to an instability channel. We finally provide the interpretation of this instability in terms of the nucleation of a bubble of nothing dressed up with a D2 charge distribution.