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It is well known that Hopf-fibre T-duality and uplift takes the D1-D5near-horizon into a class of $AdS_3 \times S^2$ geometries in 11D where theinternal space is a Calabi-Yau three-fold. Moreover, supersymmetry dictatesthat Calabi-Yau is the only permissible $SU(3)$-structure manifold.Generalising this duality chain to non-Abelian isometries, a strong parallelexists, resulting in the first explicit example of a class of $AdS_3 \timesS^2$ geometries with $SU(2)$-structure. Furthermore, the non-Abelian T-dual of$AdS_3 \times S^3 \times S^3 \times S^1$ results in a new supersymmetric $AdS_3\times S^2$ geometry, which falls outside of all known classifications. Weexplore the basic properties of the holographic duals associated to the newbackgrounds. We compute the central charges and show that they are compatiblewith a large $\mathcal{N}=4$ superconformal algebra in the infra-red.

New $AdS_3 \times S^2$ T-duals with $\mathcal{N} = (0,4)$ supersymmetry