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 ≤ 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 organized in terms of their representations under the SO(2)T × 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.

Entanglement entropy and the boundary action of edge modes

“…These exercises will reveal the nature of the edge modes in higher spin theories. It will also be nice to explore to investigate the edge mode structure in excited states of gauge theories [28,47].…”

“…We obtain the two-point function and replace r ′ = r + δ. At the end of the computation we take δ → 0 and collect the leading order divergent term in order to evaluate the entanglement entropy of edge modes [28].…”

“…In the coincident limit, the Legendre function of the second kind admits the following expansion [28]…”