$Z_N$ Orientifolds with Flux

TL;DR

This work analyzes flux-induced moduli stabilization in type IIB ${\mathbb Z}_N$ orientifolds, focusing on the dilaton-axion ${\tau}$ and complex structure moduli through the ISD condition on ${G_3}$ and the flux-generated superpotential $W=\int G_3\wedge\Omega$. By computing the flux tadpole $N_{flux}$ and constructing explicit brane configurations, the author demonstrates supersymmetric vacua with $g_s<1$ in ${\rm T}^6/{\mathbb Z}_3$, ${\rm T}^6/{\mathbb Z}_7$, and ${\rm T}^6/{\mathbb Z}_6'$ orientifolds, while noting that Kähler moduli remain unfixed in this setup. In several cases, moduli are fixed or partially fixed but require additional ingredients, such as anti-D3-branes, to balance untwisted or twisted tadpoles at the origin. The results provide concrete, analyzable models for moduli stabilization and brane configurations in simple ${\mathbb Z}_N$ toroidal orientifolds, offering avenues for semi-realistic model building and exploration of flux-related phenomena like de Sitter constructions or non-perturbative effects.

Abstract

We compute the flux induced tadpole and superpotential in various type IIB $Z_N$ compact orientifolds in order to study moduli stabilization. We find supersymmetric vacua with $g_s < 1$ and describe brane configurations with cancelled tadpoles. In some cases moduli are only partially fixed unless anti D3-branes are included.