Divisor topologies of CICY 3-folds and their applications to phenomenology

Abstract

In this article, we present a classification for the divisor topologies of the projective complete intersection Calabi-Yau (pCICY) 3-folds realized as hypersurfaces in the product of complex projective spaces. There are 7890 such pCICYs of which 7820 are favorable, and can be subsequently useful for phenomenological purposes. To our surprise we find that the whole pCICY database results in only 11 (so-called coordinate) divisors (D) of distinct topology and we classify those surfaces with their possible deformations inside the pCICY 3-fold, which turn out to be satisfying 1 ≤ h2,0(D) ≤ 7. We also present a classification of the so-called ample divisors for all the favorable pCICYs which can be useful for fixing all the (saxionic) Kähler moduli through a single non-perturbative term in the superpotential. We argue that this relatively unexplored pCICY dataset equipped with the necessary model building ingredients, can be used for a systematic search of physical vacua. To illustrate this for model building in the context of type IIB CY orientifold compactifications, we present moduli stabilization with some preliminary analysis of searching possible vacua in simple models, as a template to be adopted for analyzing models with a larger number of Kähler moduli.

Classifying divisor topologies for string phenomenology

“…In particular there are several rigid surface which satisfy unit Arithmetic genus condition and hence can be a priori suitable for generating non-perturbative superpotential effects. This properties of the divisors of THCYs is unlike the case with the other database consisting of pCICYs defined by some multi-hypersurface constraints in the product of P n 's for which no coordinate divisor was found to be rigid [20].…”

“…In this context, let us also mention that the divisor topologies of all the pCICYs have been recently computed and classified in [20] which have subsequently helped in classifying the PFFVs in [21] where it has been observed that pCICYs of K3-fibred type have more number of PFFV as compared to those which are not K3-fibred, and thus verifying the claim of [70].…”

“…Such observations have been made at multiple occasions, e.g. in the context of Kreuzer-Skarke database [29,34] as well the recent classification of divisor topologies of the complete intersection CY threefolds [20]. Further, from our explicit computations of divisor topologies of the CY geometries with 1 ≤ h 1,1 ≤ 4 which correspond to scanning through around 18000 divisor topologies of more than 2300 CY spaces, we observe that all the divisors fall in one of the following three classes of the Hodge numbers:…”

“…In the context of complete intersection CY threefolds (denoted as pCICYs which are) realised as hypersurfaces in the product of projective spaces, it has been observed in [20] that the coordinate divisors of favourable pCICYs are always simply connected and subsequently all the divisors fall in the category C 1 of (2.6). Moreover, in the context of favourable pCICYs it has been further observed that there are only 11 distinct divisor topologies arising from a total number of 57885 coordinate divisors corresponding to 7820 pCICY threefolds [20].…”

“…However some recent works in this direction have been initiated, e.g. see [15,16] for Heterotic moduli stabilization, and [17][18][19][20][21] for moduli stabilization in type IIB setups. In addition, a complete list of explicit classification of CICY orientifolds with non-trivial (1, 1)-cohomology has been also presented in [22].…”