A supersymmetric AdS${}_3$ duality

We find a dual description of the supersymmetric $SL(2,\mathbb{C})\mathrm{/}SU(2)$ WZW model as a super-winding condensate CFT, which follows simply from the bosonic AdS${}_3$ duality found in [arXiv:2104.07233]. This duality can be seen as a dimensional uplift of the mirror symmetry between the $H_3^{+}\mathrm{/}U(1)$ supercoset and $\mathcal{N}=2$ super-Liouville theory.