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

Understand

We show that the entanglement entropy of $D=4$ linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using 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 the Brietenholer-Freedman bound in $AdS_3$.
• This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture.
• Starting from the action of the 2-form on $S^1\times AdS_5$ and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator.