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

We construct and study the $AdS_3\times\text{disk}\times\text{disk}$ and $AdS_2\times\text{disk}\times\text{disk}$ solutions of $U(1)^2$-gauged supergravity in seven and six dimensions, respectively. For the construction of $AdS_3\times\text{disk}\times\text{disk}$ 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 $AdS_3\times\text{spindle}\ltimes\text{disk}$ and $AdS_2\times\text{spindle}\ltimes\text{disk}$ solutions.