Exploring Free Matrix CFT Holographies at One-Loop

We extend our recent study on the duality between stringy higher spin theories and free conformal field theories (CFTs) in the $SU\left(N\right)$ adjoint representation to other matrix models, namely the free $SO\left(N\right)$ and $Sp\left(N\right)$ adjoint models as well as the free $U\left(N\right)\times U\left(M\right)$ bi-fundamental and $O\left(N\right)\times O\left(M\right)$ bi-vector models. After determining the spectrum of the theories in the planar limit by Polya counting, we compute the one loop vacuum energy and Casimir energy for their respective bulk duals by means of the Character Integral Representation of the Zeta Function (CIRZ) method, which we recently introduced. We also elaborate on possible ambiguities in the application of this method.