Non-supersymmetric D-branes with Vanishing Cylinder Amplitudes in Asymmetric Orbifolds

We study the type II string vacua with chiral space-time SUSY constructed as asymmetric orbifolds of torus and $ K3 $ compactifications. Despite the fact that all the D-branes are non-BPS in any chiral SUSY vacua, we show that the relevant non-geometric vacua of asymmetric orbifolds allow rather generally configurations of D-branes which lead to vanishing cylinder amplitudes, implying the bose-fermi cancellation at each mass level of the open string spectrum. After working on simple models of toroidal asymmetric orbifolds, we focus on the asymmetric orbifolds of $ T^2 \times {\cal M} $, where $ {\cal M} $ is described by a general $ {\cal N} =4 $ SCFT with $ c=6 $ defined by the Gepner construction for $ K3 $. Even when the modular invariant partition functions in the bulk remain unchanged, the spectra of such non-BPS D-branes with the bose-fermi cancellation can vary significantly according to the choice of orbifolding.