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Non-perturbative and Flux superpotentials for Type I strings on the Z_3 orbifold

Massimo Bianchi, Elias Kiritsis

TL;DR

The paper addresses non-perturbative effects in Type I string theory on a Z3 orbifold with Wilson-line breaking, focusing on how D-brane instantons and closed-string fluxes generate superpotentials for both open and closed moduli. It develops a global framework to classify D-brane instantons (ED5 and ED1) and shows that ADS-like superpotentials arise from ED5 in the presence of antisymmetric Chan-Paton representations, while ED1 instantons contribute additional mass terms and other non-perturbative corrections. It derives flux-induced contributions from RR flux, Scherk-Schwarz torsion, and non-geometric fluxes, and discusses their compatibility with instanton effects and potential moduli stabilization. The work outlines a path toward stabilizing both open and closed string moduli in these vacua and points to future directions for achieving metastable de Sitter uplifts and fully consistent tadpole cancellation with the combined non-perturbative and flux sectors.

Abstract

Non-perturbative effects are studied for Type I strings on the Z_3 orbifold with Chan-Paton symmetry broken by Wilson lines. Generalizing previous analyses that have focussed on (bi)fundamentals, it is argued that (anti)symmetric representations of the resulting gauge group play a decisive role in generating an ADS-like superpotential in this and related cases. Non perturbative corrections in the closed string moduli are only allowed if properly dressed with open string fields charged under the anomalous U(1) of the orbifold. A general discussion of instanton effects in SYM and string theories is given. Non-perturbative superpotentials induced by both $ED5$'s and ED1's are analyzed. The superpotential generated by closed string fluxes, viz. Scherk-Schwarz shifts (torsion), R-R 3-form flux as well as non-geometric fluxes is derived. Some preliminary comments on the compatibility of the two kinds of superpotentials and the issue of moduli stabilization are presented.

Non-perturbative and Flux superpotentials for Type I strings on the Z_3 orbifold

TL;DR

The paper addresses non-perturbative effects in Type I string theory on a Z3 orbifold with Wilson-line breaking, focusing on how D-brane instantons and closed-string fluxes generate superpotentials for both open and closed moduli. It develops a global framework to classify D-brane instantons (ED5 and ED1) and shows that ADS-like superpotentials arise from ED5 in the presence of antisymmetric Chan-Paton representations, while ED1 instantons contribute additional mass terms and other non-perturbative corrections. It derives flux-induced contributions from RR flux, Scherk-Schwarz torsion, and non-geometric fluxes, and discusses their compatibility with instanton effects and potential moduli stabilization. The work outlines a path toward stabilizing both open and closed string moduli in these vacua and points to future directions for achieving metastable de Sitter uplifts and fully consistent tadpole cancellation with the combined non-perturbative and flux sectors.

Abstract

Non-perturbative effects are studied for Type I strings on the Z_3 orbifold with Chan-Paton symmetry broken by Wilson lines. Generalizing previous analyses that have focussed on (bi)fundamentals, it is argued that (anti)symmetric representations of the resulting gauge group play a decisive role in generating an ADS-like superpotential in this and related cases. Non perturbative corrections in the closed string moduli are only allowed if properly dressed with open string fields charged under the anomalous U(1) of the orbifold. A general discussion of instanton effects in SYM and string theories is given. Non-perturbative superpotentials induced by both 's and ED1's are analyzed. The superpotential generated by closed string fluxes, viz. Scherk-Schwarz shifts (torsion), R-R 3-form flux as well as non-geometric fluxes is derived. Some preliminary comments on the compatibility of the two kinds of superpotentials and the issue of moduli stabilization are presented.

Paper Structure

This paper contains 13 sections, 75 equations.

Table of Contents

  1. Introduction and conclusions
  2. General discussion of instanton effects
  3. Instantons in supersymmetric gauge theories
  4. Instantons in string theory
  5. Compatibility of bulk isometries and non-perturbative effects
  6. Review of type II ${\bf Z}_3$ orbifold
  7. The ${\bf Z}_3$ orientifolds with Wilson lines
  8. Non-perturbative effects in the ${\bf Z}_3$ orientifold
  9. Wrapped Euclidean D5-branes
  10. Wrapped D-strings
  11. Fluxes
  12. Scherk-Schwarz Torsion on ${\bf Z}_3$ orbifold
  13. Concluding remarks