Entanglement entropy of local gravitational quenches

Abstract

We study the time dependence of Rényi/entanglement entropies of locally excited states created by fields with integer spins $s\le 2$ in $4$ dimensions. For spins 0, 1 these states are characterised by localised energy densities of a given width which travel as a spherical wave at the speed of light. For the spin 2 case, in the absence of a local gauge invariant stress tensor, we probe these states with the Kretschmann scalar and show they represent localised curvature densities which travel at the speed of light. We consider the reduced density matrix of the half space with these excitations and develop methods which include a convenient gauge choice to evaluate the time dependence of Rényi/entanglement entropies as these quenches enter the half region. In all cases, the entanglement entropy grows in time and saturates at $\log 2$. In the limit, the width of these excitations tends to zero, the growth is determined by order $2s+1$ polynomials in the ratio of the distance from the co-dimension-2 entangling surface and time. The polynomials corresponding to quenches created by the fields can be organised in terms of their representations under the $SO(2{)}_T\times SO(2{)}_L$ symmetry preserved by the presence of the co-dimension 2 entangling surface. For fields transforming as scalars under this symmetry, the order $2s+1$ polynomial is completely determined by the spin.

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References in corpus (32)

• Evolution of Entanglement Entropy in One-Dimensional Systems
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Quantum quenches in 1+1 dimensional conformal field theories
• Holographic Local Quenches and Entanglement Density
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Quantum Entanglement of Local Operators in Conformal Field Theories
• Evolution of entanglement after a local quench
• Quantum Dimension as Entanglement Entropy in 2D CFTs
• Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects
• Quantum Entanglement of Localized Excited States at Finite Temperature
• The Holographic Nature of Null Infinity
• Mutual information after a local quench in conformal field theory
• Entanglement of Local Operators in large N CFTs
• Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
• Universality at large transverse spin in defect CFT
• Failure of the split property in gravity and the information paradox
• Notes on Quantum Entanglement of Local Operators
• Entanglement constant for conformal families
• Renyi Entropy for Local Quenches in 2D CFTs from Numerical Conformal Blocks
• Evolution of entanglement entropy in the D1-D5 brane system
• Universal corrections to entanglement entropy of local quantum quenches
• Quantum Entanglement of Fermionic Local Operators
• Entanglement entropy of gravitational edge modes
• Local quenches, bulk entanglement entropy and a unitary Page curve
• Quantum Entanglement of Locally Excited States in Maxwell Theory
• Entanglement entropy of linearized gravitons in a sphere
• Subsystem distance after a local operator quench
• Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, $p$-forms
• Local quenches and quantum chaos from higher spin perturbations
• Defining entanglement without tensor factoring: a Euclidean hourglass prescription
• Extractable entanglement from a Euclidean hourglass

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