Orientifold Calabi-Yau threefolds: divisor exchanges and multi-reflections

Abstract

Using the Kreuzer-Skarke database of 4-dimensional reflexive polytopes, we systematically constructed a new database of orientifold Calabi-Yau threefolds with h1,1(X) ≤ 12. Our approach involved non-trivial ℤ2 involutions, incorporating both divisor exchanges and multi-divisor reflections acting on the Calabi-Yau threefolds. Each proper involution results in an orientifold Calabi-Yau threefolds and we constructed 320, 386, 067 such examples. We developed a novel algorithm that significantly reduces the complexity of determining all the fixed loci under the involutions, and clarifies the types of O-planes. Our results show that under proper involutions, the majority of cases end up with O3/O7-plane systems, and most of these further admit a naive Type IIB string vacua. Additionally, a new type of free action was determined. We also computed the smoothness and the splitting of Hodge numbers in the ℤ2-orbifold limit for these orientifold Calabi-Yau threefolds.