AdS${}_3$ T-duality and evidence for $\mathcal{N}=5,6$ superconformal quantum mechanics

We construct two families of AdS${}_2$ vacua in Type IIB Supergravity performing U(1) and SL(2) T-dualities on the \text{AdS}_3 \times \text{ \widehat{$\mathbb{C}\mathbb{P}$}!!~^3} \times I solutions to Type IIA recently reported in arXiv:2304.12207. Depending on the T-duality we operate, we find two different classes of solutions of the type \text{AdS}_2 \times \text{ \widehat{$\mathbb{C}\mathbb{P}$}!!~^3} \times I $\times$ I and \text{AdS}_3 \times \text{ \widehat{$\mathbb{C}\mathbb{P}$}!!~^3} \times I $\times$ S${}^1$. This provides evidence for more general classes of solutions \text{AdS}_2 \times \text{ \widehat{$\mathbb{C}\mathbb{P}$}!!~^3} \times Σ, dual to superconformal quantum mechanics with $\mathcal{N}=5,6$ supersymmetry.