Charting the Complex Structure Landscape of F-theory

TL;DR

This paper investigates the structure of F-theory compactifications on specific Calabi--Yau fourfolds with a thrice-punctured sphere moduli space, classifying monodromies and analyzing phase behaviors at infinity.

Contribution

It enumerates all Calabi--Yau fourfolds with large complex structure and conifold points on a thrice-punctured sphere, and studies their phase structures and physical couplings.

Findings

Identified 14 monodromy tuples with quasi-unipotent monodromy.

Analyzed four phase types and computed leading periods.

Provided a computational notebook for period vector setup.

Abstract

We explore the landscape of F-theory compactifications on Calabi--Yau fourfolds whose complex structure moduli space is the thrice-punctured sphere. As a first part, we enumerate all such Calabi--Yau fourfolds under the additional requirement that it has a large complex structure and conifold point at two of the punctures. We find 14 monodromy tuples by demanding the monodromy around infinity to be quasi-unipotent. As second part, we study the four different types of phases arising at infinity. For each we consider a working example where we determine the leading periods and other physical couplings. We also included a notebook that sets up the period vectors for any of these models.