G-flux in F-theory and algebraic cycles

TL;DR

This paper develops a method to explicitly construct G4 fluxes in F-theory using algebraic cycles, enabling direct computation of physical quantities and establishing connections with type IIB string theory.

Contribution

It introduces a novel approach to identify algebraic cycles in elliptic Calabi-Yau fourfolds for constructing G4 fluxes and relates these to a unified sheaf-theoretic framework.

Findings

Explicit G4 fluxes constructed via algebraic cycles.

Successful matching with type IIB results in weak coupling limits.

Proposed generalizations suggest a unified sheaf description.

Abstract

We construct explicit G4 fluxes in F-theory compactifications. Our method relies on identifying algebraic cycles in the Weierstrass equation of elliptic Calabi-Yau fourfolds. We show how to compute the D3-brane tadpole and the induced chirality indices directly in F-theory. Whenever a weak coupling limit is available, we compare and successfully match our findings to the corresponding results in type IIB string theory. Finally, we present some generalizations of our results which hint at a unified description of the elliptic Calabi-Yau fourfold together with the four-form flux G4 as a coherent sheaf. In this description the close link between G4 fluxes and algebraic cycles is manifest.