Bubbles of nothing and AdS instabilities

In this contribution we review the ideas and results presented in the articles arXiv:2002.01764 and arXiv:2110.08276 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 AdS$_4$ vacuum arising in a compactification of massive IIA supergravity on a $S^6$ and preserving G$_2$ symmetry. This vacuum has been shown to have a fully stable KK spectrum and also be protected against brane-jet decays. In this framework we discuss a bubble solution in massive IIA connected to the G$_2$-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.