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

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