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

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