Orientifold Calabi-Yau threefolds with divisor involutions and string landscape

Abstract

We establish an orientifold Calabi-Yau threefold database for h1,1(X) ≤ 6 by considering non-trivial ℤ2 divisor exchange involutions, using a toric Calabi-Yau database (www.rossealtman.com/tcy). We first determine the topology for each individual divisor (Hodge diamond), then identify and classify the proper involutions which are globally consistent across all disjoint phases of the Kähler cone for each unique geometry. Each of the proper involutions will result in an orientifold Calabi-Yau manifold. Then we clarify all possible fixed loci under the proper involution, thereby determining the locations of different types of O-planes. It is shown that under the proper involutions, one typically ends up with a system of O3/O7-planes, and most of these will further admit naive Type IIB string vacua. The geometries with freely acting involutions are also determined. We further determine the splitting of the Hodge numbers into odd/even parity in the orbifold limit. The final result is a class of orientifold Calabi-Yau threefolds with non-trivial odd class cohomology ($$ {h}_{-}^{1,1} $$ h − 1 , 1 (X/σ*) ≠ 0).

Systematics of perturbatively flat flux vacua

“…The reason behind this goal is to examine if such vacua are unique (or accidental and limited to just few CY geometries) or there is some (statistical) pattern in the sense of counting the number of PFFV. For that purpose, we consider the CY geometries arising from the triangulation of four-dimensional reflexive polytopes of the Kreuzer-Skarke (KS) database [47], and use the relevant topological data from the collection in [48,49]. Given our current focus being limited to the stabilization of complex structure moduli and the axio-dilaton, we will use 39 CY geometries with h 1,1 = 2 assuming that their respective mirrors would be the ones used to compactify the type IIB superstring theory.…”

The LVS Parametric Tadpole Constraint

“…By contrast, non-local D7-tadpole cancellation produced values in the larger range [−132, −12]. Moreover, the study of toric orientifold Calabi-Yaus with h 1,1 ≤ 6 in [66] gave 30,0]. This was based only on the divisor exchange involution and local D7-tadpole cancellation.…”

“…It is the fact that in CICYs the topology of each divisor is relatively simple and the largest Euler number of a divisor is modest: χ(D a ) max = 80 [64,67]. By contrast, in the toric setting even with h 1,1 (X) ≤ 6, the highest Euler number that gives an integer contribution to the tadpole is χ(D a ) max = 504 [66]. Even if we only consider a reflection on this divisor and cancel the D7-tadpole locally, it will contribute −126 to the tadpole.…”

“…Even if we only consider a reflection on this divisor and cancel the D7-tadpole locally, it will contribute −126 to the tadpole. A distribution of Euler numbers of divisors in the orientifold Calabi-Yau database of [66] is displayed in Fig. 1.…”

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

“…However, our current aim is not to present the full intersection polynomial, but only to illustrate that the divisor topology analysis using NIDs is consistent with the database in [46] where this example has been shown to indeed possess three possible orientifolds which can give h 1,1 − = 7. 7 Analyzing around 23000 reflexive polytopes leading to more than 500000 triangulations and nearly 100000 distinct CY geometries with h 1,1 ≤ 6 of the KS database [4], it turns out that one can only have h 1,1 − ≤ 3 for the dataset in [11]. However, this upper limit of h 1,1 − being 3 could be anticipated, given that h 1,1 (CY ) ≤ 6 for that dataset, and we need pairs of NIDs for constructing odd divisor D− in the basis.…”