Orientifold Calabi-Yau Threefolds: Divisor Exchanges and Multi-Reflections

TL;DR

This paper systematically constructs a large database of orientifold Calabi-Yau threefolds using involutions on reflexive polytopes, revealing common O-plane configurations and new free actions, with implications for string vacua.

Contribution

It introduces a novel algorithm for identifying fixed loci under involutions, enabling the construction of over 320 million orientifold Calabi-Yau examples with detailed geometric analysis.

Findings

Majority have O3/O7-plane systems

Most admit naive Type IIB vacua

Discovered a new type of free action

Abstract

Using the Kreuzer-Skarke database of 4-dimensional reflexive polytopes, we systematically constructed a new database of orientifold Calabi-Yau threefolds with $h^{1,1}(X) \leq 12$. Our approach involved non-trivial $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$-orbifold limit for these orientifold Calabi-Yau threefolds.