On topological F-theory

TL;DR

This paper constructs a topological F-theory on a specific 8-manifold, derives its action, and explores dualities and flux backgrounds through dimensional reduction and symmetry analysis.

Contribution

It introduces a topological version of F-theory on a Spin(7) manifold and analyzes its dualities and flux configurations via Hitchin's flow and symmetry considerations.

Findings

Derived an 8D action for topological F-theory.

Showed duality transformations from modular symmetry.

Explored flux backgrounds in 6D target space actions.

Abstract

We consider the construction of a topological version of F-theory on a particular $Spin(7)$ 8-manifold which is a Calabi-Yau 3-fold times a 2-torus. We write an action for this theory in eight dimensions and reduce it to lower dimensions using Hitchin's gradient flow method. A symmetry of the eight-dimensional theory which follows from modular transformations of the torus induces duality transformations of the variables of the topological A- and B-models. We also consider target space form actions in the presence of background fluxes in six dimensions.