Asymmetric orbifolds with vanishing one-loop vacuum energy

TL;DR

This work constructs and classifies non-supersymmetric Type II string vacua on toroidal asymmetric orbifolds that exhibit vanishing one-loop vacuum energy, $V_1=0$, sector-by-sector via preserved supercharge-like operators. It shows that, for finite Abelian point groups, only $\mathbb{Z}_k\times\mathbb{Z}_k$ with $k=2,3,4$ can realize the mechanism, and then builds explicit Abelian models ($\mathbb{Z}_2\times\mathbb{Z}_2$, $\mathbb{Z}_3\times\mathbb{Z}_3$, $\mathbb{Z}_4\times\mathbb{Z}_4$) along with non-Abelian examples ($S_3\times\mathbb{Z}_3$, $D_6$), introducing carefully chosen shifts to lift potential tachyons and gravitini while preserving modular invariance. Detailed anomaly analyses using level matching and bordism show that the constructions are consistent, tachyon-free, and, in several cases, maintain $V_1=0$; some models also indicate possible higher-loop cancellations. The results offer a concrete stringy mechanism to realize small or vanishing vacuum energy without target-space SUSY, with implications for moduli stabilization and the landscape of nonsupersymmetric string vacua, while highlighting open questions about higher-loop behavior and full non-Abelian classifications.

Abstract

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 $\mathbb{Z}_k \times \mathbb{Z}_k$ 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.