Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches

TL;DR

This paper analyzes entanglement entropy in 2d CFT for excited states and local quenches, showing universal stress tensor contributions and matching holographic calculations, thus illustrating entanglement thermalization in holographic microstates.

Contribution

It provides a universal stress tensor contribution to entanglement entropy in 2d CFT and demonstrates its agreement with holographic duals for heavy states and quenches.

Findings

Universal stress tensor contribution dominates in large central charge theories.

Entanglement entropy matches holographic geodesic calculations.

Entanglement entropy thermalizes in individual holographic microstates.

Abstract

We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that entanglement entropy thermalizes in individual microstates of holographic CFTs. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.