Entanglement entropy of gravitational edge modes

Abstract

We consider the linearised graviton in $4d$ Minkowski space and decompose it into tensor spherical harmonics and fix the gauge. The Gauss law of gravity implies that certain radial components of the Riemann tensor of the graviton on the sphere label the superselection sectors for the graviton. We show that among these 6 normal components of the Riemann tensor, 2 are related locally to the algebra of gauge-invariant operators in the sphere. From the two-point function of these components of the Riemann tensor on $S^2$ we compute the logarithmic coefficient of the entanglement entropy of these superselection sectors across a spherical entangling surface. For sectors labelled by each of the two components of the Riemann tensor these coefficients are equal and their total contribution is given by $-\frac{16}{3}$. We observe that this coefficient coincides with that extracted from the edge partition function of the massless spin-2 field on the 4-sphere when written in terms of its Harish-Chandra character. As a preliminary step, we also evaluate the logarithmic coefficient of the entanglement entropy from the superselection sectors labelled by the radial component of the electric field of the $U(1)$ theory in even $d$ dimensions. We show that this agrees with the corresponding coefficient of the edge Harish-Chandra character of the massless spin-1 field on $S^d$.

arXiv commentTypos corrected

References in corpus (21)

• Local subsystems in gauge theory and gravity
• Remarks on entanglement entropy for gauge fields
• Decomposition of entanglement entropy in lattice gauge theory
• Entanglement entropy of electromagnetic edge modes
• Entanglement entropy in gauge theories and the holographic principle for electric strings
• On The Entanglement Entropy For Gauge Theories
• Geometric entropy and edge modes of the electromagnetic field
• Entanglement entropy and nonabelian gauge symmetry
• Aspects of Entanglement Entropy for Gauge Theories
• Local phase space and edge modes for diffeomorphism-invariant theories
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• The entanglement of distillation for gauge theories
• Entanglement entropy for a Maxwell field: Numerical calculation on a two dimensional lattice
• Gravity Edges Modes and Hayward Term
• Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory
• Entanglement entropy of a Maxwell field on the sphere
• Duality for symmetric second rank tensors. II. The linearized gravitational field
• Generalized Symmetries of the Graviton
• Entanglement entropy of linearized gravitons in a sphere
• Superselection Sectors of Gravitational Subregions
• Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, $p$-forms

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