Universal AdS Black Holes in Theories with 16 Supercharges and Their Microstates

We provide a universal microscopic counting for the microstates of asymptotically AdS black holes and strings that arise as solutions half-maximal gauged supergravity in 4 5 dimensions. These can be embedded all M-theory type II string backgrounds with an vacuum 16 supercharges infinite set examples dual to $\mathcal{N}=2$ $\mathcal{N}=4$ conformal field theories four three dimensions, respectively. The is it performed by either studying large $N$ limit relevant supersymmetric index theory or using charged Cardy formula.