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

TL;DR

This paper analyzes string loop corrections to the Kaehler potential in Type IIB Calabi-Yau flux compactifications, revealing an extended no-scale structure that causes leading corrections to vanish in the scalar potential.

Contribution

It provides a low-energy interpretation of conjectured loop corrections and demonstrates their vanishing contribution to the scalar potential for general Calabi-Yaus.

Findings

Leading loop corrections to the scalar potential always vanish for homogeneous functions of degree -2.

The extended no-scale structure is confirmed through multiple examples.

A simple formula for 1-loop scalar potential correction is derived.

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.