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

Understand

It is well known that Hopf-fibre T-duality and uplift takes the D1-D5 near-horizon into a class of $AdS_3 \times S^2$ geometries in 11D where the internal space is a Calabi-Yau three-fold.

• Moreover, supersymmetry dictates that Calabi-Yau is the only permissible $SU(3)$-structure manifold.
• Generalising this duality chain to non-Abelian isometries, a strong parallel exists, resulting in the first explicit example of a class of $AdS_3 \times S^2$ 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.