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Flux interactions on D-branes and instantons

Marco Billo', Livia Ferro, Marialuisa Frau, Francesco Fucito, Alberto Lerda, Jose F. Morales

TL;DR

This work provides a first-principles world-sheet derivation of flux-induced fermionic couplings on D-branes and their instantons, unifying space-filling and instantonic sectors under a disk-amplitude framework. By carefully implementing boundary conditions, twists, and magnetization, the authors reproduce known supergravity results and extend them to twisted boundary conditions and Euclidean branes. In a concrete Type IIB ${ m Z}_2 imes{ m Z}_2$ orbifold with fractional branes, they connect four-dimensional soft terms to flux backgrounds via gauge kinetic functions and moduli F-terms, demonstrating that IASD fluxes generate gaugino masses while ISD fluxes lift instanton zero modes. The analysis clarifies how fluxes influence non-perturbative effects and moduli stabilization, with implications for brane-world models and exotic instantons, and sets the stage for further study in less supersymmetric setups and flavored sectors.

Abstract

We provide a direct world-sheet derivation of the couplings of NS-NS and R-R fluxes to various types of D-branes (including instantonic ones) by evaluating disk amplitudes among two open string vertex operators at a generic brane intersection and one closed string vertex representing the background fluxes. This world-sheet approach is in full agreement with the derivation of the flux couplings in the brane effective actions based on supergravity methods, but it is applicable also to more general brane configurations involving fields with twisted boundary conditions. As an application, we consider an orbifold compactification of Type IIB string theory with fractional D-branes preserving N=1 supersymmetry and study the flux-induced fermionic mass terms both on space-filling branes and on instantonic ones. Our results show the existence of a relation between the soft supersymmetry breaking and the lifting of some instanton fermionic zero-modes, which may lead to new types of non-perturbative couplings in brane-world models.

Flux interactions on D-branes and instantons

TL;DR

This work provides a first-principles world-sheet derivation of flux-induced fermionic couplings on D-branes and their instantons, unifying space-filling and instantonic sectors under a disk-amplitude framework. By carefully implementing boundary conditions, twists, and magnetization, the authors reproduce known supergravity results and extend them to twisted boundary conditions and Euclidean branes. In a concrete Type IIB orbifold with fractional branes, they connect four-dimensional soft terms to flux backgrounds via gauge kinetic functions and moduli F-terms, demonstrating that IASD fluxes generate gaugino masses while ISD fluxes lift instanton zero modes. The analysis clarifies how fluxes influence non-perturbative effects and moduli stabilization, with implications for brane-world models and exotic instantons, and sets the stage for further study in less supersymmetric setups and flavored sectors.

Abstract

We provide a direct world-sheet derivation of the couplings of NS-NS and R-R fluxes to various types of D-branes (including instantonic ones) by evaluating disk amplitudes among two open string vertex operators at a generic brane intersection and one closed string vertex representing the background fluxes. This world-sheet approach is in full agreement with the derivation of the flux couplings in the brane effective actions based on supergravity methods, but it is applicable also to more general brane configurations involving fields with twisted boundary conditions. As an application, we consider an orbifold compactification of Type IIB string theory with fractional D-branes preserving N=1 supersymmetry and study the flux-induced fermionic mass terms both on space-filling branes and on instantonic ones. Our results show the existence of a relation between the soft supersymmetry breaking and the lifting of some instanton fermionic zero-modes, which may lead to new types of non-perturbative couplings in brane-world models.

Paper Structure

This paper contains 32 sections, 198 equations, 2 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Flux interactions on D-branes from string diagrams
  3. Boundary conditions and reflection matrices
  4. Open and closed string vertices
  5. Open String Vertices
  6. Closed String Vertices
  7. The string correlator with R-R and NS-NS fluxes
  8. R-R flux
  9. NS-NS flux
  10. Flux couplings with untwisted open strings ($\vec{\vartheta}=0$)
  11. Unmagnetized D-branes
  12. Unmagnetized Euclidean branes
  13. Magnetized branes
  14. Flux-induced fermionic mass and lifting of instanton zero-modes
  15. Flux couplings with twisted open strings ($\vec{\vartheta}\not =0$)
  16. ...and 17 more sections

Figures (2)

  • Figure 1: Quadratic coupling of untwisted, $a)$, and twisted, $b)$, open string states to closed string fluxes.
  • Figure 2: The quiver diagram encoding the field content and the charges for fractional D-branes of the local orbifold $\mathbb{C}^3/(\mathbb{Z}_2\times\mathbb{Z}_2)$. The dots represent the branes associated with the irrep $R_A$ of the orbifold group. A stack of $N_A$ such branes supports a $\mathrm{U}(N_A)$ gauge theory. An oriented link from the $A$-th to the $B$-th dot corresponds to a chiral multiplet $\phi^{AB}$ transforming in the $(N_A,\overline N_B)$ representation of the gauge group and in the $R_A\,R_B^{-1}$ representation of the orbifold group.