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D-brane instantons and the effective field theory of flux compactifications

Angel M. Uranga

TL;DR

This work develops a 4d effective field theory framework to describe how fluxes affect euclidean D-brane instantons, showing that flux superpotentials lift heavy moduli and dress the original instanton vertices, turning multi-fermion F-terms into non-perturbative superpotentials. The approach provides a global, moduli-space–spanning description, applicable to geometric and non-geometric fluxes, and matches results from microscopic analyses by integrating out massive fields and dressing instanton amplitudes. It also uncovers formal connections to the bulk-boundary map in open-closed topological string theory and to ${\cal N}=1$ special geometry, offering a coherent picture of instanton effects across flux backgrounds. The framework is demonstrated through explicit D3-instanton examples, including magnetized branes and non-geometric fluxes, and is shown to reproduce known no-go results while predicting new lifting mechanisms via non-geometric fluxes.

Abstract

We provide a description of the effects of fluxes on euclidean D-brane instantons purely in terms of the 4d effective action. The effect corresponds to the dressing of the effective non-perturbative 4d effective vertex with 4d flux superpotential interactions, generated when the moduli fields made massive by the flux are integrated out. The description in terms of effective field theory allows a unified description of non-perturbative effects in all flux compactifications of a given underlying fluxless model, globally in the moduli space of the latter. It also allows us to describe explicitly the effects on D-brane instantons of fluxes with no microscopic description, like non-geometric fluxes. At the more formal level, the description has interesting connections with the bulk-boundary map of open-closed two-dimensional topological string theory, and with the $\NN=1$ special geometry.

D-brane instantons and the effective field theory of flux compactifications

TL;DR

This work develops a 4d effective field theory framework to describe how fluxes affect euclidean D-brane instantons, showing that flux superpotentials lift heavy moduli and dress the original instanton vertices, turning multi-fermion F-terms into non-perturbative superpotentials. The approach provides a global, moduli-space–spanning description, applicable to geometric and non-geometric fluxes, and matches results from microscopic analyses by integrating out massive fields and dressing instanton amplitudes. It also uncovers formal connections to the bulk-boundary map in open-closed topological string theory and to special geometry, offering a coherent picture of instanton effects across flux backgrounds. The framework is demonstrated through explicit D3-instanton examples, including magnetized branes and non-geometric fluxes, and is shown to reproduce known no-go results while predicting new lifting mechanisms via non-geometric fluxes.

Abstract

We provide a description of the effects of fluxes on euclidean D-brane instantons purely in terms of the 4d effective action. The effect corresponds to the dressing of the effective non-perturbative 4d effective vertex with 4d flux superpotential interactions, generated when the moduli fields made massive by the flux are integrated out. The description in terms of effective field theory allows a unified description of non-perturbative effects in all flux compactifications of a given underlying fluxless model, globally in the moduli space of the latter. It also allows us to describe explicitly the effects on D-brane instantons of fluxes with no microscopic description, like non-geometric fluxes. At the more formal level, the description has interesting connections with the bulk-boundary map of open-closed two-dimensional topological string theory, and with the special geometry.

Paper Structure

This paper contains 18 sections, 55 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Lifting fermion zero modes is integrating out massive moduli
  3. The basic idea
  4. A simple field theory analog
  5. Example: deformation fermion zero modes and 3-form fluxes
  6. The setup
  7. The microscopic viewpoint: Lifting zero modes by fluxes
  8. Effective field theory viewpoint: integrating out moduli
  9. Applications
  10. Revisiting a no-go result: $U(1)$ instantons and 3-form fluxes
  11. Magnetized $U(1)$ instantons
  12. Magnetized D3-brane instantons and 3-form fluxes
  13. Magnetized D3-brane instantons and non-geometric fluxes
  14. Worldsheet bulk-boundary map: D-brane zero modes as zero modes of 4d moduli
  15. Comments on the role of ${\cal N}=1$ special geometry for D3-brane instantons
  16. ...and 3 more sections

Figures (1)

  • Figure 1: The supergraph describing the integration out of the multiplets $U$.