Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields

We establish the relation of partition functions conformal higher spin fields on Weyl equivalent spaces in $d=4$ dimension. express function graviton and as an integral over characters $S^1\times AdS_3$, $S^4$, $AdS_4$. observe that spins hyperbolic cylinders differs from $S^4$ by `edge' contribution. The logarithmic coefficient obtained character $AdS_4$ is half $S^4$. evaluate entanglement entropy dimension twist operator cylinder. co-dimension two enables us to find a linear between Hofman-Maldacena variables which we use show non-unitarity theory. spectrum quasinormal modes bulk contains additional distinct states compared unitary massless fields.