AdS$_3$ T-duality and evidence for ${\cal N}=5,6$ 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{CP}}\!\!~^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{CP}}\!\!~^3$} \times $ I $\times$ I and $\text{AdS}_3 \times \text{$ \widehat{\mathbb{CP}}\!\!~^3$} \times $ I $\times$ S$^1$. This provides evidence for more general classes of solutions $\text{AdS}_2 \times \text{$ \widehat{\mathbb{CP}}\!\!~^3$} \times \Sigma $, dual to superconformal quantum mechanics with ${\cal N}=5,6$ supersymmetry.