Systematics of string loop corrections in type IIB Calabi-Yau flux compactifications

We study the behaviour of the string loop corrections to the N = 1 4D supergravity Kähler potential that occur in flux compactifications of IIB string theory on general Calabi-Yau three-folds. We give a low energy interpretation for the conjecture of Berg, Haack and Pajer for the form of the loop corrections to the Kähler potential. We check the consistency of this interpretation in several examples. We show that for arbitrary Calabi-Yaus, the leading contribution of these corrections to the scalar potential is always vanishing, giving an ''extended no-scale structure''. This result holds as long as the corrections are homogeneous functions of degree -2 in the 2-cycle volumes. We use the Coleman-Weinberg potential to motivate this cancellation from the viewpoint of low-energy field theory. Finally we give a simple formula for the 1-loop correction to the scalar potential in terms of the tree-level Kähler metric and the conjectured correction to the Kähler potential. We illustrate our ideas with several examples. A companion paper will use these results in the study of Kähler moduli stabilisation.