Systematics of perturbatively flat flux vacua for CICYs

Abstract

In this paper, we extend the analysis of scanning the perturbatively flat flux vacua (PFFV) for the type IIB orientifold compactifications on the mirror of the projective complete intersection Calabi-Yau (pCICY) 3-folds, which are realized as hypersurfaces in the product of complex projective spaces. The main objective of this scan is to investigate the behaviour of PFFV depending on the nature of CY 3-folds in the light of the observations made in [1] where it has been found that K3-fibered CY 3-folds have significantly large number of physical vacua as compared to other geometries. For this purpose, we present the PFFV statistics for all the 36 pCICYs with h1,1 = 2 and classify them into two categories of being K3-fibered model and non K3-fibered model. We subsequently confirm that all the K3-fibered models have a significantly large number of PFFV leading to physical vacua by fixing the axio-dilaton by non-perturbative effects, while only a couple of non K3-fibered models have such physical vacua. For h1,1 = 2 case, we have found that there are five pCICY 3-folds with the suitable exchange symmetry leading to the so-called exponentially flat flux vacua (EFFV) which are protected against non-perturbative prepotential effects as well. By exploring the underlying exchange symmetries in the favorable CY 3-folds with h1,1 ≥ 3 in the dataset of 7820 pCICYs, we have found that there are only 13 spaces which can result in EFFV configurations, and therefore most of the CY 3-folds are a priory suitable for fixing the dilaton valley of the flat vacua using the non-perturbative prepotential contributions.