On non-supersymmetric stable marginal deformations in AdS$_3$/CFT$_2$

We discuss a continuous family of non-supersymmetric AdS$_3\times S^3\times{\rm T^4}$ vacua in heterotic and type II supergravities whose complete Kaluza-Klein spectrum is computed and found to be free from instabilities. This family is protected as well against some non-perturbative decay channels, and as such it provides the first candidate for a non-supersymmetric holographic conformal manifold in 2$d$. We also describe the operators realising the deformations in the worldsheet and boundary CFT's.