Gopakumar-Vafa Hierarchies in Winding Inflation and Uplifts

TL;DR

This paper introduces a novel mechanism for winding inflation and de Sitter uplifts using a hierarchy of Gopakumar-Vafa invariants in Calabi-Yau threefolds, supported by a comprehensive database of invariants.

Contribution

It demonstrates how to realize the necessary scalar potential structure through Gopakumar-Vafa invariants rather than moduli tuning, and provides explicit databases of these invariants.

Findings

Constructed a database of genus 0 Gopakumar-Vafa invariants up to degree 10 for complete intersection Calabi-Yau's.

Identified redundancies in the CICY list up to Picard number 13.

Proposed a new inflation and uplift mechanism using Calabi-Yau hierarchies.

Abstract

We propose a combined mechanism to realize both winding inflation and de Sitter uplifts. We realize the necessary structure of competing terms in the scalar potential not via tuning the vacuum expectation values of the complex structure moduli, but by a hierarchy of the Gopakumar-Vafa invariants of the underlying Calabi-Yau threefold. To show that Calabi-Yau threefolds with the prescribed hierarchy actually exist, we explicitly create a database of all the genus $0$ Gopakumar-Vafa invariants up to total degree $10$ for all the complete intersection Calabi-Yau's up to Picard number $9$. As a side product, we also identify all the redundancies present in the CICY list, up to Picard number $13$. Both databases can be accessed at this link: https://www.desy.de/~westphal/GV_CICY_webpage/GVInvariants.html .