Asymmetric orbifolds with vanishing one-loop vacuum energy

We present a systematic study of non-supersymmetric type II toroidal asymmetric orbifolds with vanishing vacuum energy at one-loop in string perturbation theory. These are engineered through the conservation of a supercharge-like operator in each individual sector in the orbifold sum, despite the overall explicit breaking of spacetime SUSY. We provide a full classification of such orbifolds with finite Abelian point-group, which can only admit ℤ_k × ℤ_k point group with k = 2, 3, 4. We present detailed constructions, alongside other examples with non-Abelian point group. For some of these models, it is possible that this cancellation persists at higher loops.