Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Instantons and Holomorphic Couplings in Intersecting D-brane Models

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

TL;DR

The paper addresses holomorphic couplings in Type IIA orientifolds with intersecting D6-branes by establishing a one-loop non-renormalisation theorem, detailing toroidal threshold corrections, and linking D2-instanton (E2) amplitudes to holomorphic data. It shows that the holomorphic gauge kinetic function receives one-loop contributions only from ${\cal N}=2$ sectors, while ${\cal N}=1$ thresholds are non-holomorphic and must be absorbed into moduli redefinitions that cancel $\sigma$-model anomalies. The authors then formulate how E2-instantons can generate holomorphic superpotential terms, as well as potential instanton-induced corrections to gauge kinetic functions and FI-terms, with the holomorphic physics encoded in disc and annulus amplitudes and their relation to threshold corrections. Together, these results provide a structured, holomorphy-consistent framework for perturbative and non-perturbative corrections in intersecting D-brane vacua, clarifying when and how instantons can contribute to the effective action and how to extract holomorphic data from non-holomorphic string amplitudes.

Abstract

We clarify certain aspects and discuss extensions of the recently introduced string D-instanton calculus (hep-th/0609191). The one-loop determinants are related to one-loop open string threshold corrections in intersecting D6-brane models. Utilising a non-renormalisation theorem for the holomorphic Wilsonian gauge kinetic functions, we derive a number of constraints for the moduli dependence of the matter field Kaehler potentials of intersecting D6-brane models on the torus. Moreover, we compute string one-loop corrections to the Fayet-Iliopoulos terms on the D6-branes finding that they are proportional to the gauge threshold corrections. Employing these results, we discuss the issue of holomorphy for E2-instanton corrections to the superpotential. Eventually, we discuss E2-instanton corrections to the gauge kinetic functions and the FI-terms.

Instantons and Holomorphic Couplings in Intersecting D-brane Models

TL;DR

The paper addresses holomorphic couplings in Type IIA orientifolds with intersecting D6-branes by establishing a one-loop non-renormalisation theorem, detailing toroidal threshold corrections, and linking D2-instanton (E2) amplitudes to holomorphic data. It shows that the holomorphic gauge kinetic function receives one-loop contributions only from sectors, while thresholds are non-holomorphic and must be absorbed into moduli redefinitions that cancel -model anomalies. The authors then formulate how E2-instantons can generate holomorphic superpotential terms, as well as potential instanton-induced corrections to gauge kinetic functions and FI-terms, with the holomorphic physics encoded in disc and annulus amplitudes and their relation to threshold corrections. Together, these results provide a structured, holomorphy-consistent framework for perturbative and non-perturbative corrections in intersecting D-brane vacua, clarifying when and how instantons can contribute to the effective action and how to extract holomorphic data from non-holomorphic string amplitudes.

Abstract

We clarify certain aspects and discuss extensions of the recently introduced string D-instanton calculus (hep-th/0609191). The one-loop determinants are related to one-loop open string threshold corrections in intersecting D6-brane models. Utilising a non-renormalisation theorem for the holomorphic Wilsonian gauge kinetic functions, we derive a number of constraints for the moduli dependence of the matter field Kaehler potentials of intersecting D6-brane models on the torus. Moreover, we compute string one-loop corrections to the Fayet-Iliopoulos terms on the D6-branes finding that they are proportional to the gauge threshold corrections. Employing these results, we discuss the issue of holomorphy for E2-instanton corrections to the superpotential. Eventually, we discuss E2-instanton corrections to the gauge kinetic functions and the FI-terms.

Paper Structure

This paper contains 13 sections, 65 equations, 5 figures.

Table of Contents

  1. Introduction
  2. A non-renormalisation theorem
  3. One-loop thresholds for intersecting D6-branes on $\mathbb T^6$
  4. Fayet-Iliopoulos terms
  5. Wilsonian gauge kinetic function and $\sigma$-model anomalies
  6. Holomorphic gauge couplings for toroidal models
  7. Universal threshold corrections
  8. Holomorphic E2-instanton amplitudes
  9. Half-BPS instantons
  10. Superpotential contributions
  11. Instanton corrections to the gauge kinetic functions
  12. Instanton corrections to the FI-terms
  13. Conclusions

Figures (5)

  • Figure 1: Relation between instantonic one-loop amplitudes and corresponding gauge threshold corrections
  • Figure 2: Relation between instantonic Möbius amplitude and corresponding gauge threshold corrections
  • Figure 3: Deformations of an instanton which is invariant under the orientifold projection
  • Figure 4: Annulus diagram for E2-instanton correction to $f_a$. The upper indices give the ghost number of the vertex operators.
  • Figure 5: Annulus diagram for E2-instanton correction to $\xi_a$. The upper indices give the ghost number of the vertex operators.