Abstract
In this article, we present a systematic analysis of the so-called perturbatively flat flux vacua (PFFV) for the mirror Calabi-Yau (CY) 3-folds ( {overset{sim }{X}}_3 ) with h1,1( {overset{sim }{X}}_3 ) = 2 arising from the Kreuzer-Skarke database of the four-dimensional reflexive polytopes. We consider the divisor topologies of the CY 3-folds for classifying the subsequent models into three categories; (i) models with the so-called Swiss-cheese structure, (ii) models with the K3-fibered structure, and (iii) the remaining ones which we call as models of “Hybrid type”. In our detailed analysis of PFFV we find that for a given fixed value of the D3 tadpole charge Nflux, the K3-fibered mirror CY 3-folds have significantly larger number of such PFFV as compared to those which have Swiss-cheese structure, while the Hybrid type models have a mixed behavior. We also compute the Gopakumar-Vafa invariants necessary for fixing the flat valley in the weak string-coupling and large complex-structure regime by using the non-perturbative effects, which subsequently reduce the number of physically trustworthy vacua quite significantly. Moreover, we find that there are some examples in which the PFFV are protected even at the leading orders of the non-perturbative effects due to the some underlying symmetry in the CY geometry, which we call as “Exponentially flat flux vacua”. We also present a new class of PFFV using the S-duality arguments.
Highlights
In the context of type IIB orientifold compactifications, moduli stabilization has attracted huge amount of interests since the past two decades [1–8]
In our detailed and systematic analysis, we find that there is a significant number of perturbatively flat flux vacua (PFFV), though we observed that the K3-fibered CY geometries can have reasonably large number of PFFV configurations as compared to the other CY geometries
We find that there are a couple of CY geometries having some peculiar types of PFFV which are protected against non-perturbative effects as well, and we call such vacua as “exponentially flat flux vacua” (EFFV)
Summary
In the context of type IIB orientifold compactifications, moduli stabilization has attracted huge amount of interests since the past two decades [1–8] This is usually a two-step process where in the first step complex structure moduli and the axio-dilaton are stabilized by turning on background fluxes [9–13] while in the second step Kähler moduli are stabilized using sub-leading corrections [14, 15]. In order to fix the flat direction by using non-perturbative effects in the prepotential we compute the Gopakumar-Vafa invariants [52, 53] for all the 39 CY geometries and have subsequently utilized them in getting physical vacua in the large complex-structure and weak string-coupling regime.
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