Orientifolds with discrete torsion

TL;DR

This paper explores how discrete torsion can be incorporated into four-dimensional N=1 type IIB orientifolds, analyzing consistency conditions, classification, and explicit spectra for different models.

Contribution

It provides a classification of orientifold models with discrete torsion, including spectrum and tadpole cancellation conditions, based on real projective representations.

Findings

Discrete torsion parameter epsilon can only be ±1.

Four types of orientifold constructions are identified.

Explicit spectra and tadpole conditions are derived for each model.

Abstract

We show how discrete torsion can be implemented in D=4, N=1 type IIB orientifolds. Some consistency conditions are found from the closed string and open string spectrum and from tadpole cancellation. Only real values of the discrete torsion parameter are allowed, i.e. epsilon=+-1. Orientifold models are related to real projective representations. In a similar way as complex projective representations are classified by H^2(Gamma,C^*)=H^2(Gamma,U(1)), real projective representations are characterized by H^2(Gamma,R^*)=H^2(Gamma,Z_2). Four different types of orientifold constructions are possible. We classify these models and give the spectrum and the tadpole cancellation conditions explicitly.