Cardy-Verlinde formula from boundary matrix model

Cardy-Verlinde (CV) formula relates the entropy of a conformal field theory (CFT) in arbitrary dimensions to its total energy (with an appropriate insertion of additional internal energy for charged systems) and Casimir energy. While several aspects of the CV formula have been tested directly for weakly coupled CFTs, the aim of the present paper is to verify it in the strongly coupled regime, by employing a phenomenological matrix model, which captures the features of the $\mathcal{N}=4$, $SU(N)$ Super Yang-Mills theory on $S^3$ at finite temperature and chemical potential at large $N$.