Magnetized E3-brane instantons in F-theory

TL;DR

This paper analyzes E3-brane instantons in F-theory, focusing on how world-volume fluxes influence zero modes and superpotential generation, with explicit examples and a detailed geometric interpretation.

Contribution

It clarifies the structure of E3-E3 zero modes with fluxes, incorporates SL(2,Z) monodromies, and generalizes superpotential index calculations in F-theory.

Findings

Fluxes can lift zero modes, enabling superpotential contributions.

Explicit example on P^3 demonstrates flux contributions from non-rigid divisors.

Generalized index formulas include flux effects, matching known results.

Abstract

We discuss E3-brane instantons in N=1 F-theory compactifications to four dimensions and clarify the structure of E3-E3 zero modes for general world-volume fluxes. We consistently incorporate SL(2,Z) monodromies and highlight the relation between F-theory and perturbative IIB results. We explicitly show that world-volume fluxes can lift certain fermionic zero-modes, whose presence would prevent the generation of non-perturbative superpotential terms, and we discuss in detail the geometric interpretation of the zero-mode lifting mechanism. We provide a IIB derivation of the index for generation of superpotential terms and of its modification to include world-volume fluxes, which reproduces and generalizes available results. We apply our general analysis to the explicit, though very simple, example of compactification on P^3 and its orientifold weak-coupling limit. In particular, we provide an example in which a non-rigid divisor with fluxes contributes to the superpotential.