Brane instantons and fluxes in F-theory

TL;DR

This work derives a quadratic, topologically twisted fermionic action for Euclidean D3-brane instantons in F-theory flux vacua, incorporating bulk and world-volume fluxes, warping, and axio-dilaton effects. By dissecting left- and right-handed sectors, it identifies how fluxes lift or preserve fermionic zero modes and clarifies the SL(2,$\mathbb{Z}$) transformation properties, including off-shell subtleties linked to M-theory uplift. The authors connect zero-mode counting to twisted cohomology and provide a framework to compute non-perturbative F-terms and their dependence on SUSY-breaking bulk fluxes, with a clear perturbative regime in the large-volume limit. They also present a detailed M5-brane uplift, mapping E3-field content to vertical M5-form structures and highlighting the role of $G_4$ flux and diffeomorphism-invariance challenges. Overall, the results advance understanding of non-perturbative effects in flux compactifications and their consistency with 4D effective theories.

Abstract

We study the combined effect of world-volume and background fluxes on Euclidean D3-brane instantons in F-theory compactifications. We derive an appropriate form of the fermionic effective action, in which the fermions are topologically twisted and the dynamical effect of fluxes, non-trivial axio-dilaton and warping is taken into account. We study the structure of fermionic zero modes, which determines the form of possible non-perturbative superpotential and F-terms in the four-dimensional effective action. Invariance under SL(2,Z) is discussed in detail, which allows for an interpretation of the results in terms of the dual M5-brane instanton in the M-theory picture. We also provide the perturbative IIB description in the orientifold limit, when available. Furthermore, we consider the possible inclusion of supersymmetry breaking bulk fluxes and discuss its implications.