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

TL;DR

This paper investigates non-perturbative effects and flux-induced superpotentials in Type I string theories on the Z_3 orbifold, highlighting the role of (anti)symmetric representations and open string fields in moduli stabilization.

Contribution

It extends previous analyses by including (anti)symmetric representations and open string fields in the study of non-perturbative superpotentials for Type I strings on the Z_3 orbifold.

Findings

(Anti)symmetric representations are crucial for ADS-like superpotentials.

Non-perturbative corrections require open string fields charged under anomalous U(1).

Fluxes induce superpotentials that impact moduli stabilization.

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.