Four-dimensional N=1 Z_N X Z_M Orientifolds

TL;DR

This work analyzes four-dimensional $N=1$ orientifolds with abelian orbifold groups $Z_N$ × $Z_M$ by deriving tadpole cancellation conditions via Chan-Paton representations and computing both closed- and open-string massless spectra. The authors establish a general orientifold framework, provide explicit gamma-matrix solutions for several models, and show that some cases (notably $Z_2$ × $Z_4$ and $Z_4$ × $Z_4$) have no consistent tadpole solutions due to representation-theoretic constraints. They present detailed spectra for models with varying orbifold actions, including the gauge groups and matter content arising from 99, $5_i5_i$, and mixed sectors. The results map the landscape of consistent four-dimensional $N=1$ orientifolds and highlight stringent consistency conditions, suggesting possible heterotic duals and avenues for extensions such as discrete torsion or alternative group actions.

Abstract

We calculate the tadpole equations and their solutions for a class of four-dimensional orientifolds with orbifold group Z_N X Z_M, and we present the massless bosonic spectra of these models. Surprisingly we find no consistent solutions for the models with Z_2 X Z_4 and Z_4 X Z_4 orbifold groups.