Warped Kahler potentials and fluxes

The four-dimensional effective theory for type IIB warped flux compactifications proposed in [1] is completed by taking into account the backreaction of the Kahler moduli on the three-form fluxes. The only required modification consists in a flux dependent contribution to the chiral fields parametrising the Kahler moduli. The resulting supersymmetric effective theory satisfies the no-scale condition and consistently combines previous partial results present in the literature. Similar results hold for M-theory warped compactifications on Calabi-Yau fourfolds, whose effective field theory and Kahler potential are also discussed.