# PQ Axiverse

I construct a landscape of vacua of string theory and study the resulting ensemble of N-axion effective theories. This is an incarnation of the string axiverse that is detailed enough to reveal patterns in low-energy couplings. We find that in Calabi-Yau compactifications, assuming that all length-scales and cycle sizes are comparable is not tenable: the geometry enforces hierarchies by powers of N. These powers appear in the distributions of couplings, such as instanton actions and axion decay constants. One important consequence is that in this landscape the strong CP problem is automatically solved by the Peccei-Quinn mechanism. The leading Planck-scale effects that could spoil the PQ solution are certain D-brane instantons whose actions are set by cycle sizes. We compute these instantons explicitly and show that for N >> 10 they are negligible, because of the N-dependent hierarchies of cycle sizes. These same hierarchies allow the QCD axion decay constant to readily lie in the allowed range.