Entanglement entropy of local gravitational quenches

TL;DR

This paper analyzes how entanglement entropy evolves over time for local gravitational and field excitations in four dimensions, revealing universal growth patterns and saturation at log 2, with a focus on spins 0, 1, and 2.

Contribution

It introduces a method to compute the time-dependent Rényi/entanglement entropies for local excitations of spins 0, 1, and 2, including gauge-invariant curvature probes for spin 2 in 4D.

Findings

Entanglement entropy grows and saturates at log 2 for all examined cases.

Growth is characterized by polynomials of order 2s+1 in the ratio of distance to time.

Polynomials are organized by their representations under SO(2)_T × SO(2)_L symmetry.

Abstract

We study the time dependence of R\'{e}nyi/entanglement entropies of locally excited states created by fields with integer spins $s \leq 2$ 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 R\'{e}nyi/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.