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

Abstract

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 $S^1\times Ad{S}_3$. The mass of the constant mode on $S^1$ saturates the Brietenholer-Freedman bound in $Ad{S}_3$. 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 $S^1\times Ad{S}_5$ and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal $p$-forms in even dimensions it obeys the expected relations with the coefficients determining the $3$-point function of the stress tensor of these fields.

52 pages, published version, improved treatment of the graviton

References in corpus (8)

• Towards a derivation of holographic entanglement entropy
• Gauge invariant Lagrangian formulation of higher spin massive bosonic field theory in AdS space
• Quantum W-symmetry in AdS_3
• Twist operators in higher dimensions
• Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• $C_T$ for conformal higher spin fields from partition function on conically deformed sphere
• The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields

Cited by in corpus (11)

• A proposal for 3d quantum gravity and its bulk factorization
• Generalized Symmetries of the Graviton
• Entanglement entropy of gravitational edge modes
• Pseudo Entropy in $U(1)$ gauge theory
• Partition functions of higher derivative conformal fields on conformally related spaces
• Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields
• Dynamical Edge Modes in $p$-form Gauge Theories
• Entanglement entropy of local gravitational quenches
• Entanglement entropy of a Rarita-Schwinger field in a sphere
• Extractable entanglement from a Euclidean hourglass
• Partition functions of $p$-forms from Harish-Chandra characters