General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation

TL;DR

This paper investigates the conditions under which large volume minima can be achieved in flux compactifications of IIB string theory, emphasizing the role of topological features and string loop corrections in moduli stabilization.

Contribution

It identifies necessary topological conditions and analyzes the impact of string loop corrections on stabilizing moduli at exponentially large volumes in Calabi-Yau compactifications.

Findings

Negative Euler number is necessary for large volume minima.

String loop corrections are crucial for stabilizing certain moduli.

Large volume minima are realizable in fibration Calabi-Yaus with stabilized moduli.

Abstract

We study the topological conditions for general Calabi-Yaus to get a non-supersymmetric AdS exponentially large volume minimum of the scalar potential in flux compactifications of IIB string theory. We show that negative Euler number and the existence of at least one blow-up mode resolving point-like singularities are necessary and sufficient conditions for moduli stabilisation with exponentially large volumes. We also analyse the general effects of string loop corrections on this scenario. While the combination of alpha' and nonperturbative corrections are sufficient to stabilise blow-up modes and the overall volume, quantum corrections are needed to stabilise other directions transverse to the overall volume. This allows exponentially large volume minima to be realised for fibration Calabi-Yaus, with the various moduli of the fibration all being stabilised at exponentially large values. String loop corrections may also play a role in stabilising 4-cycles which support chiral matter and cannot enter directly into the non-perturbative superpotential. We illustrate these ideas by studying the scalar potential for various Calabi-Yau three-folds including K3 fibrations and briefly discuss the potential phenomenological and cosmological implications of our results.