Systematics of String Loop Corrections in Type IIB Calabi-Yau Flux Compactifications

TL;DR

The paper analyzes leading string-loop corrections to the Type IIB Kähler potential in Calabi–Yau flux compactifications, showing that when these corrections are homogeneous of degree $-2$ in 2-cycle volumes an extended no-scale structure cancels the leading 1-loop contribution to the scalar potential. It provides a low-energy Coleman–Weinberg perspective and derives a general 1-loop potential formula in terms of the tree-level Kähler metric and the loop correction $\delta K$, with explicit checks in multiple Calabi–Yau examples. The work also outlines how the conjectured form of $\delta K$ from Berg–Haack–Pajer aligns with the low-energy theory and how the corrections scale in concrete geometries, informing moduli stabilization schemes such as the Large Volume Scenario. The findings emphasize that loop corrections, though subleading to $\alpha'$ effects, can play important roles in stabilizing Kähler moduli and lifting flat directions, while preserving consistency with low-energy effective theory and Coleman–Weinberg expectations.

Abstract

We study the behaviour of the string loop corrections to the N=1 4D supergravity Kaehler 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 Kaehler 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 Kaehler metric and the correction to the Kaehler potential. We illustrate our ideas with several examples. A companion paper will use these results in the study of Kaehler moduli stabilisation.