Airy functions from quantum M-theory

We show that Airy function partition functions for M2-brane theories may be derived from relative equivariant localization of quantum M-theory. The eleven-dimensional Chern–Simons coupling gives the cubic term in the grand potential, while the $X_8$ correction gives the charge shift. Fixing the M2-brane charge turns the localized M-theory path integral into an Airy integral. In this way we derive the ABJM result, its toric Calabi–Yau generalizations, and gravitational blocks for black holes and other spacetimes, up to the prefactor and non-perturbative corrections.