M5-branes and D4-branes wrapped on a direct product of spindle and Riemann surface

Abstract: We construct multi-charged $AdS_3\times{\Sigma}\times\Sigma_{\mathfrak{g}}$ and $AdS_2\times{\Sigma}\times\Sigma_{\mathfrak{g}}$ solutions from M5-branes and D4-branes wrapped on a direct product of spindle, ${\Sigma}$, and Riemann surface, $\Sigma_{\mathfrak{g}}$. Employing uplift formula, we obtain these solutions by uplifting the multi-charged $AdS_3\times{\Sigma}$ and $AdS_2\times{\Sigma}$ solutions to seven and six dimensions, respectively. We further uplift the solutions to eleven-dimensional and massive type IIA supergravity and calculate the holographic central charge and the Bekenstein-Hawking entropy, respectively. We perform the gravitational block calculations and, for the $AdS_3\times{\Sigma}\times\Sigma_{\mathfrak{g}}$ solutions, the result precisely matches the holographic central charge from the supergravity solutions.