Type I Vacua from Diagonal $Z_3$-Orbifolds

TL;DR

This work analyzes open descendants of diagonal $Z_3$ orbifolds, tying their perturbative consistency to discrete geometric moduli. By combining the orbifold action with a T-duality, it shows two fixed-point resolutions ($I_1$ and $I_2$) yield distinct unoriented projections, enabling a tractable construction of Type I vacua in $D=6$ and $D=4$. The resulting spectra are parameterized by the fixed-point survival number $n$, with $SO(8)$ gauge symmetry in six dimensions and non-chiral $Sp(4)$ symmetry in four dimensions, all satisfying anomaly and tadpole consistency. The analysis suggests a rich landscape of diagonal orbifold orientifolds, extendable to $Z_N$ cases and potentially including anti-branes, while remaining constrained by conformal field theory on surfaces with boundaries and crosscaps.

Abstract

We discuss the open descendants of diagonal irrational $Z_3$ orbifolds, starting from the $c=2$ case and analyzing six-dimensional and four-dimensional models. As recently argued, their consistency is linked to the presence of geometric discrete moduli. The different classes of open descendants, related to different resolutions of the fixed-point ambiguities, are distinguished by the number of geometric fixed points surviving the unoriented projection.