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Magnetized E3-brane instantons in F-theory

Massimo Bianchi, Andres Collinucci, Luca Martucci

TL;DR

This work analyzes magnetized E3-brane instantons in F-theory, focusing on how general world-volume fluxes modify the E3-E3 fermionic zero-mode structure while incorporating SL(2,Z) monodromies and the IIB/M-theory dictionary. By deriving the fluxless action and then extending to magnetized cases, the authors construct a flux-modified index and show how certain zero modes can be lifted, enabling non-perturbative superpotential contributions even for non-rigid divisors. They connect the IIB results to the dual M5-brane index and Ext groups, providing a coherent framework that unifies perturbative and non-perturbative pictures, including an explicit P^3 example. The work demonstrates that fluxes expand the landscape of instanton effects and offer new avenues for moduli stabilization and phenomenology in global F-theory compactifications.

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.

Magnetized E3-brane instantons in F-theory

TL;DR

This work analyzes magnetized E3-brane instantons in F-theory, focusing on how general world-volume fluxes modify the E3-E3 fermionic zero-mode structure while incorporating SL(2,Z) monodromies and the IIB/M-theory dictionary. By deriving the fluxless action and then extending to magnetized cases, the authors construct a flux-modified index and show how certain zero modes can be lifted, enabling non-perturbative superpotential contributions even for non-rigid divisors. They connect the IIB results to the dual M5-brane index and Ext groups, providing a coherent framework that unifies perturbative and non-perturbative pictures, including an explicit P^3 example. The work demonstrates that fluxes expand the landscape of instanton effects and offer new avenues for moduli stabilization and phenomenology in global F-theory compactifications.

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.

Paper Structure

This paper contains 24 sections, 185 equations, 1 figure.

Table of Contents

  1. Introduction and summary of the results
  2. A short review on F-theory vacua
  3. Generalities on F-theory compactifications
  4. Supersymmetric structures
  5. Orientifold limit
  6. Relation with the M-theory viewpoint
  7. A working example
  8. E3-instantons without fluxes: the IIB perspective
  9. Fluxless E3-fermionic action
  10. Zero-modes
  11. M5-brane index from IIB perspective
  12. Comparison with the dual M-theory result
  13. $\chi_{\rm E3}$ as the perturbative Ext index
  14. Implementation in the working example
  15. Magnetized E3-instantons
  16. ...and 9 more sections

Figures (1)

  • Figure 1: Schematic description of the reorganization of the E3 fermionic zero modes in terms of the corresponding zero modes on the dual M5-brane. Here $h^i({\rm E3})\equiv h^i(D)$, $h^i_Q({\rm E3})\equiv h^i_Q(D) = \dim H^i(D, K_X)$ and $h^{i}({\rm M5})\equiv\dim H^i(\hat{D}, {\cal O}_{\hat{D}})\equiv\dim H^{0,i}_{\bar{\partial}}(\hat{D})$.