Transdimensional Tunneling in the Multiverse

Topology-changing transitions between vacua of different effective dimensionality are studied in the context of a 6-dimensional Einstein-Maxwell theory. The landscape of this theory includes a $6d$ de Sitter vacuum ($d{S}_6$), a number of $d{S}_4\times S_2$ and $Ad{S}_4\times S_2$ vacua, and a number of $Ad{S}_2\times S_4$ vacua. We find that compactification transitions $dS_6 \to AdS_2 \times S_4$ occur through the nucleation of electrically charged black hole pairs, and transitions from $d{S}_6$ to $d{S}_4\times S_2$ and $AdS_4 \times S_2$ occur through the nucleation of magnetically charged spherical black branes. We identify the appropriate instantons and describe the spacetime structure resulting from brane nucleation.