Discrete torsion in non-geometric orbifolds and their open-string descendants

TL;DR

This work analyzes non-geometric, left-right asymmetric orbifolds of type II strings and their type I descendants, focusing on discrete torsion as a tunable knob that alters supersymmetry and spectra. It introduces a simplifying open-string ansatz that aligns transverse-channel amplitudes to yield consistent tadpole cancellation and then applies it to several models, including Z2 and Z3 twists in four and six dimensions. The paper uncovers both supersymmetric and non-supersymmetric open-string sectors, highlights twisted open-string states, and discusses rank reductions of Chan-Paton groups via discrete torsion and T-duality identifications. These results illuminate how non-geometric backgrounds can be treated algebraically with boundary and crosscap data and suggest avenues for connecting to Gepner models and non-perturbative solitons.

Abstract

We discuss some Z_N^L x Z_N^R orbifold compactifications of the type IIB superstring to D= 4,6 dimensions and their type I descendants. Although the Z_N^L x Z_N^R generators act asymmetrically on the chiral string modes, they result into left-right symmetric models that admit sensible unorientable reductions. We carefully work out the phases that appear in the modular transformations of the chiral amplitudes and identify the possibility of introducing discrete torsion. We propose a simplifying ansatz for the construction of the open-string descendants in which the transverse-channel Klein-bottle, annulus and Moebius-strip amplitudes are numerically identical in the proper parametrization of the world-sheet. A simple variant of the ansatz for the Z_2^L x Z_2^R orbifold gives rise to models with supersymmetry breaking in the open-string sector.