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We show that the entanglement entropy of $D=4$ linearized gravitons across asphere recently computed by Benedetti and Casini coincides with that obtainedusing the Kaluza-Klein tower of traceless transverse massive spin-2 fields on$S^1\times AdS_3$. The mass of the constant mode on $S^1$ saturates theBrietenholer-Freedman bound in $AdS_3$. This condition also ensures that theentanglement entropy of higher spins determined from partition functions on thehyperbolic cylinder coincides with their recent conjecture. Starting from theaction of the 2-form on $S^1\times AdS_5$ and fixing gauge, we evaluate theentanglement entropy across a sphere as well as the dimensions of thecorresponding twist operator. We demonstrate that the conformal dimensions ofthe corresponding twist operator agrees with that obtained using theexpectation value of the stress tensor on the replica cone. For conformal$p$-forms in even dimensions it obeys the expected relations with thecoefficients determining the $3$-point function of the stress tensor of thesefields.

Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, $p$-forms