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

TL;DR

The paper demonstrates that entanglement entropy for heavy-state excitations and local quenches in large-$c$ 2d CFTs is governed by universal stress-tensor contributions captured by the Virasoro identity block. By using the replica trick and relating conformal blocks to geodesic lengths in AdS$_3$ with defects, the authors achieve precise agreement with holographic calculations for both BTZ black hole microstates and conical defects, including time-dependent quenches. The work extends the framework to finite-circle geometries with angular potentials and to dynamical quenches, showing that monodromy of Virasoro blocks drives entanglement growth and supports the covariant holographic entanglement entropy prescription. Overall, it provides strong evidence that entanglement in holographic CFT microstates thermalizes and that bulk geometric intuition emerges from the identity Virasoro block in sparse, large-$c$ theories.

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.

Figures (5)

• Figure 1: Configuration of $2n$$\psi$'s on a multisheeted surface, branched across the red cut which extends along an arc on the unit circle from 1 to $z$.
• Figure 2: Left: Two ways to analytically continue the approximate expression for the twist correlator $G_n(z,\bar{z})$ around the singularity in the complex $z$-plane. Right: Two geodesics in the singular geometry \ref{['defge']} with the same endpoints. The choice of analytic continuation in evaluating the block translates into a choice of winding around the singularity at $z= 0$.
• Figure 3: Two geodesics in the BTZ geometry (at fixed time) with the same endpoints. The choice of channel in the CFT corresponds to a choice of winding around the black hole horizon.
• Figure 4: Setup for the local operator quench. The initial state has a localized excitation near $x = 0$, which propagates outward and eventually increases the entanglement entropy of region $A$.
• Figure 5: Left: Analytic continuation in the complex time plane. Continuing along the solid curve gives the correlator with the first two operators in time ordering, and the second gives these operators in anti-time-ordering. Right: Lorentzian configuration of operators where we cannot use the $\sigma \tilde{\sigma}$ OPE.