Orientifold Calabi-Yau Threefolds with Divisor Involutions and String Landscape

TL;DR

This paper constructs a database of orientifold Calabi-Yau threefolds with divisor involutions, classifying their topologies, fixed loci, and resulting string vacua for models with small Hodge number $h^{1,1} \, \leq\, 6.

Contribution

It provides a systematic classification of orientifold Calabi-Yau threefolds with divisor exchange involutions, including topology, fixed loci, and odd cohomology, expanding the string landscape database.

Findings

Classified proper involutions and fixed loci for Calabi-Yau threefolds with $h^{1,1} \leq 6$.

Identified systems with $O3/O7$-planes suitable for Type IIB vacua.

Determined geometries with freely acting involutions and odd cohomology.

Abstract

We establish an orientifold Calabi-Yau threefold database for $h^{1,1}(X) \leq 6$ by considering non-trivial $\mathbb{Z}_{2}$ divisor exchange involutions, using a toric Calabi-Yau database (http://www.rossealtman.com/toriccy/). 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 K\"ahler 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 $h^{1,1}_{-}(X / \sigma^*) \neq 0$.