The entropy of radiation for local quenches in higher dimensions

TL;DR

This paper analyzes the dynamics of radiation and entanglement entropy following a local quench in higher-dimensional conformal field theories, combining analytic estimates and holographic methods to understand their time evolution.

Contribution

It provides new analytic estimates and holographic computations of entanglement entropy dynamics in higher-dimensional CFTs with local quenches, including boundary cases.

Findings

Derived early- and late-time entanglement entropy behavior.

Established an upper bound for entanglement entropy at all times.

Computed holographic entanglement entropy showing a Page-like curve.

Abstract

We investigate the real time dynamics of the radiation produced by a local quench in a $d$-dimensional conformal field theory (CFT) with $d>2$. Using the interpretation of the higher-dimensional twist operator as a conformal defect, we study the time evolution of the entanglement entropy of the radiation across a spherical entangling surface. We provide an analytic estimate for the early- and late-time behavior of the entanglement entropy and derive an upper bound valid at all times. We extend our analysis to the case of a boundary CFT (BCFT) and derive similar results through a detailed discussion of the setup with two conformal defects (the boundary and the twist operator). We conclude with a holographic analysis of the process, computing the time evolution of the holographic entanglement entropy (HEE) as the area of the Ryu-Takayanagi surface in a backreacted geometry. This gives a Page-like curve in agreement with the early- and late-time results obtained with CFT methods. The extension to a holographic BCFT setup is generically hard and we consider the case of a tensionless end-of-the-world brane.