Computing Brane and Flux Superpotentials in F-theory Compactifications

TL;DR

This paper explicitly computes the flux superpotential in F-theory compactifications, incorporating all complex structure moduli and brane deformations, and analyzes classical and instanton contributions using mirror symmetry.

Contribution

It provides a detailed calculation of the flux superpotential in F-theory, including brane and flux effects, and explores dual heterotic descriptions.

Findings

Explicit flux superpotential depending on all complex structure moduli

Matching F-theory results to D5-branes in local limits

Analysis of classical and instanton contributions via mirror symmetry

Abstract

In four-dimensional F-theory compactifications with N=1 supersymmetry the fields describing the dynamics of space-time filling 7-branes are part of the complex structure moduli space of the internal Calabi-Yau fourfold. We explicitly compute the flux superpotential in F-theory depending on all complex structure moduli, including the 7-brane deformations and the field corresponding to the dilaton-axion. Since fluxes on the 7-branes induce 5-brane charge, a local limit allows to effectively match the F-theory results to a D5-brane in a non-compact Calabi-Yau threefold with threeform fluxes. We analyze the classical and instanton contributions to the F-theory superpotential using mirror symmetry for Calabi-Yau fourfolds. The F-theory compactifications under consideration also admit heterotic dual descriptions and we discuss the identification of the moduli in this non-perturbative duality.