Computing Brane and Flux Superpotentials in F-theory Compactifications

TL;DR

The authors compute the flux-induced superpotential for F-theory compactifications on elliptically fibered Calabi–Yau fourfolds, incorporating both closed-string and seven-brane moduli as complex-structure deformations. They leverage mirror symmetry to evaluate classical and instanton contributions and demonstrate how fourfold periods encode the open-string brane data, reproducing D5/D7-brane superpotentials in the local limit. By constructing explicit elliptic fourfold mirror pairs with few complex structure moduli, they identify a consistent split of moduli and fluxes that matches threefold periods and open disk invariants, and they connect the F-theory setup to heterotic duals via spectral-cover data. The work provides explicit $G_4$-flux choices that realize the full flux-and-brane superpotential and offers a framework for studying flux vacua and non-perturbative dualities in F-theory phenomenology.

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.

Figures (1)

• Figure 1: Toric base and Harvey-Lawson Lagrangians for non-compact $\mathds{P}^2$