# Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds

## TL;DR

This paper examines the swampland distance conjecture in the moduli space of one-parameter Calabi-Yau threefolds, confirming its validity at certain infinite-distance points through explicit hypergeometric calculations.

## Contribution

It provides evidence that the swampland distance conjecture holds at K- and M-points in one-parameter Calabi-Yau threefolds, using explicit hypergeometric models.

## Key findings

- SDC fulfilled at K- and M-points in studied models
- Explicit hypergeometric calculations support the conjecture
- Supports broader validity of SDC in Calabi-Yau moduli spaces

## Abstract

We investigate the swampland distance conjecture (SDC) in the complex moduli space of type II compactifications on one-parameter Calabi-Yau threefolds. This class of manifolds contains hundreds of examples and, in particular, a subset of 14 geometries with hypergeometric differential Picard-Fuchs operators. Of the four principal types of singularities that can occur - specified by their limiting mixed Hodge structure - only the K-points and the large radius points (or more generally the M-points) are at infinite distance and therefore of interest to the SDC. We argue that the conjecture is fulfilled at the K- and the M-points, including models with several M-points, using explicit calculations in hypergeometric models which contain typical examples of all these degenerations. Together with previous work on the large radius points, this suggests that the SDC is indeed fulfilled for one-parameter Calabi-Yau spaces.