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D-brane Instantons in 4D Supersymmetric String Vacua

Nikolas Akerblom, Ralph Blumenhagen, Dieter Lust, Maximilian Schmidt-Sommerfeld

TL;DR

The paper surveys D-brane instantons in 4D supersymmetric string vacua, focusing on Type IIA orientifolds with intersecting D6-branes and Euclidean E2-branes. It develops and applies an instanton calculus to compute charged matter superpotential couplings, shows how holomorphic Yukawa terms arise despite non-holomorphic intermediate steps, and links one-loop instanton corrections to holomorphic gauge kinetic functions through gauge-threshold analyses and Kaplunovsky–Louis relations. It provides explicit results for the $T^6/\mathbb{Z}_2\times\mathbb{Z}_2$ orbifold and discusses conditions under which instantons can modify the gauge kinetic function beyond perturbation theory. The work highlights the importance of zero-mode structure (universal, deformation, and charged) and the role of orientifold projections in enabling or forbidding non-perturbative effects, with implications for neutrino masses, Yukawa textures, and gauge couplings in string compactifications.

Abstract

We review some aspects of D-instantons in intersecting D-brane models. In particular, we present applications of the recently proposed instanton calculus to computations of charged matter superpotential couplings and corrections to the gauge kinetic function in the low energy effective action of type IIA orientifolds. As an interesting byway, we also discuss how one-loop corrections to the gauge kinetic function can be deduced from gauge threshold corrections in the type IIA setting.

D-brane Instantons in 4D Supersymmetric String Vacua

TL;DR

The paper surveys D-brane instantons in 4D supersymmetric string vacua, focusing on Type IIA orientifolds with intersecting D6-branes and Euclidean E2-branes. It develops and applies an instanton calculus to compute charged matter superpotential couplings, shows how holomorphic Yukawa terms arise despite non-holomorphic intermediate steps, and links one-loop instanton corrections to holomorphic gauge kinetic functions through gauge-threshold analyses and Kaplunovsky–Louis relations. It provides explicit results for the orbifold and discusses conditions under which instantons can modify the gauge kinetic function beyond perturbation theory. The work highlights the importance of zero-mode structure (universal, deformation, and charged) and the role of orientifold projections in enabling or forbidding non-perturbative effects, with implications for neutrino masses, Yukawa textures, and gauge couplings in string compactifications.

Abstract

We review some aspects of D-instantons in intersecting D-brane models. In particular, we present applications of the recently proposed instanton calculus to computations of charged matter superpotential couplings and corrections to the gauge kinetic function in the low energy effective action of type IIA orientifolds. As an interesting byway, we also discuss how one-loop corrections to the gauge kinetic function can be deduced from gauge threshold corrections in the type IIA setting.

Paper Structure

This paper contains 12 sections, 30 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Zero modes of the charged matter field coupling instanton calculus
  3. Universal zero modes:
  4. Deformation zero modes:
  5. Charged zero modes:
  6. Threshold corrections and the holomorphic gauge kinetic function
  7. A non-renormalization theorem for the gauge kinetic function
  8. Gauge threshold corrections and one-loop corrections to the gauge kinetic function
  9. Example: The $T^6/\mathbb{Z}_2\times\mathbb{Z}_2$ orbifold
  10. Holomorphy of the instanton-induced superpotential
  11. Instanton corrections to the gauge kinetic function
  12. Further developments

Figures (3)

  • Figure 1: Visualization of the origin of the various zero modes. A D6-brane is shown in light blue, while an E2-brane is represented as a black blob in Minkowski space together with a line in the internal space. The E2-brane gives rise to: a) universal zero modes, and possibly b) deformation zero modes as well as c) charged zero modes.
  • Figure 2: Relation between instantonic one-loop amplitudes and corresponding   gauge  threshold corrections.
  • Figure 3: Annulus diagram for E2-instanton correction to $f_a$.