M5-branes and D4-branes wrapped on disk $\times$ disk and spindle $⋉$ disk

We construct and study the $Ad{S}_3\times \text{disk}\times \text{disk}$ and $Ad{S}_2\times \text{disk}\times \text{disk}$ solutions of $U(1{)}^2$-gauged supergravity in seven and six dimensions, respectively. For the construction of $Ad{S}_3\times \text{disk}\times \text{disk}$ solutions, we employ the previously constructed consistent truncation of seven-dimensional gauged supergravity on a disk. We uplift the solutions to eleven-dimensional and massive type IIA supergravity, respectively, and study the disk geometry of the solutions. We perform flux quantizations and calculate the holographic central charge and the Bekenstein-Hawking entropy, respectively. In a similar manner, we present the $Ad{S}_3\times \text{spindle}⋉\text{disk}$ and $Ad{S}_2\times \text{spindle}⋉\text{disk}$ solutions.