Searching for Coleman-de Luccia bubbles in AdS compactifications

Coleman-de Luccia transitions are spontaneous processes of nucleation of bubbles within metastable gravitational vacua including in their interior a true stable vacuum. From the perspective of lower-dimensional gauged supergravities obtained by truncating type II and M theory, these instantonic processes are represented by smooth domain walls featured by de Sitter foliations. These geometries must connect two different anti-de Sitter (AdS) vacua in such a way that the wall is defined by an interior and an exterior. We propose a first-order formulation for such radial flows and present two fully backreacted examples of gravitational instantons obtained through this technique, beyond the thin-wall approximation. In the first, we consider minimal 7D supergravity describing the truncation of M theory over a squashed four-sphere and admitting two AdS7 vacua, one supersymmetric and the other not. Second, we apply the same strategy to 6D Romans supergravity obtained with consistent truncation of massive IIA supergravity. Also in this case we derive a de Sitter domain wall interpolating between the Brandhuber-Oz vacuum and the nonsupersymmetric AdS6 vacuum of the theory.