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

We discuss some Z(N)(L) X Z(N)(R) orbifold complifications 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 Mobius-strip amplitudes are numerically identical in the proper parametrization of the world-sheet. A simple Variant of the ansatz fur the Z(2)(L) X Z(2)(R) orbifold gives rise to models with supersymmetry breaking in the open-string sector. (C) Elsevier Science B.V. All rights reserved.