Domain walls and superpotentials from M-theory on Calabi-Yau three-folds

Compactification of M-theory in the presence of G-fluxes yields N = 2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza–Klein reduction of the eleven-dimensional action on a Calabi–Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents five-branes wrapped over holomorphic cycles. This solution has a "running volume" and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS₅ vacuum of the 5-dimensional supergravity.