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 AdS 7 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 AdS 6 vacuum of the theory.