Radiation, entanglement and islands from a boundary local quench

TL;DR

This paper investigates the entanglement and energy density of radiation after a local quench in boundary conformal field theories, using both CFT predictions and holographic duals, revealing universal behaviors and the role of islands in unitarity preservation.

Contribution

It introduces a universal form for entanglement entropy after a local quench and demonstrates its consistency with holographic models, highlighting the formation of islands for unitarity.

Findings

Universal early- and late-time entanglement behavior predicted by OPE.

Analytical bounds on entanglement valid throughout evolution.

Holographic results agree with CFT predictions and show island formation.

Abstract

We study the entanglement and the energy density of the radiation emitted after a local quench in a boundary conformal field theory. We use the operator product expansion (OPE) to predict the early- and late-time behavior of the entanglement entropy and we find, under mild assumptions, a universal form for the leading term, which we test on some treatable two-dimensional examples. We also derive a general upper bound on the entanglement, valid along the full time evolution. In two dimensions, the bound is computed analytically, while in higher dimensions it is evaluated at early and late time via the OPE. These CFT predictions are then compared with a doubly-holographic setup where the CFT is interpreted as a reservoir for the radiation produced on an end-of-the-world brane. After finding the gravitational dual of a boundary local quench, we compute the time evolution of the holographic entanglement entropy, whose late-time behavior is in perfect agreement with the CFT predictions. In the brane+bath picture, unitarity of the time evolution is preserved thanks to the formation of an island. The holographic results can be recovered explicitly from the island formula, in the limit where the tension of the brane is close to the maximal value.