$G_4$ Flux, Algebraic Cycles and Complex Structure Moduli Stabilization

TL;DR

This paper constructs specific $G_4$ fluxes to stabilize all complex structure moduli of a sextic Calabi-Yau fourfold at the Fermat point, offering a new approach that bypasses complex differential equation solving.

Contribution

It introduces a method to stabilize complex structure moduli using algebraic cycles at a specific point, avoiding traditional Picard-Fuchs equation solutions.

Findings

Successfully stabilizes all 426 moduli at the Fermat point

Identifies tension between tadpole cancellation and moduli stabilization

Symmetric fluxes often lead to flat directions

Abstract

We construct $G_4$ fluxes that stabilize all of the 426 complex structure moduli of the sextic Calabi-Yau fourfold at the Fermat point. Studying flux stabilization usually requires solving Picard-Fuchs equations, which becomes unfeasible for models with many moduli. Here, we instead start by considering a specific point in the complex structure moduli space, and look for a flux that fixes us there. We show how to construct such fluxes by using algebraic cycles and analyze flat directions. This is discussed in detail for the sextic Calabi-Yau fourfold at the Fermat point, and we observe that there appears to be tension between M2-tadpole cancellation and the requirement of stabilizing all moduli. Finally, we apply our results to show that even though symmetric fluxes allow to automatically solve most of the F-term equations, they typically lead to flat directions.