On Classifying the Divisor Involutions in Calabi-Yau Threefolds

TL;DR

This paper classifies specific Calabi-Yau threefolds with small Hodge number that have divisor pairs related by involutions, aiming to support odd moduli in string compactifications for particle physics and cosmology models.

Contribution

It provides a detailed classification of Calabi-Yau threefolds with divisor exchange involutions and explores their potential for string model building, especially in LARGE volume scenarios.

Findings

Identified Calabi-Yau threefolds with divisor pairs under involutions.

Analyzed symmetry properties of divisors using Stanley-Reisner ideals.

Presented examples with swiss-cheese volume forms for moduli stabilization.

Abstract

In order to support the odd moduli in models of (type IIB) string compactification, we classify the Calabi-Yau threefolds with h^{1,1}<=4 which exhibit pairs of identical divisors, with different line-bundle charges, mapping to each other under possible divisor exchange involutions. For this purpose, the divisors of interest are identified as completely rigid surface, Wilson surface, K3 surface and some other deformation surfaces. Subsequently, various possible exchange involutions are examined under the symmetry of Stanley-Reisner Ideal. In addition, we search for the Calabi-Yau theefolds which contain a divisor with several disjoint components. Under certain reflection involution, such spaces also have nontrivial odd components in (1,1)-cohomology class. String compactifications on such Calabi-Yau orientifolds with non-zero h^{1,1}_-(CY_3/\sigma) could be promising for concrete model building in both particle physics and cosmology. In the spirit of using such Calabi-Yau orientifolds in the context of LARGE volume scenario, we also present some concrete examples of (strong/weak) swiss-cheese type volume form.