Holographic Entanglement Entropy For a Large Class of States in 2D CFT

TL;DR

This paper investigates entanglement entropy in a broad class of 2D CFT states at large central charge, demonstrating it aligns with holographic predictions via the Ryu-Takayanagi formula.

Contribution

It extends the understanding of holographic entanglement entropy to a wide class of 2D CFT states using monodromy analysis and Chern-Simons gravity.

Findings

Entanglement entropy matches the Ryu-Takayanagi formula.

Monodromy analysis effectively computes entropy for complex states.

Holographic duality holds for states created by heavy operators.

Abstract

In this paper, we study the entanglement entropy in a large class of states of two-dimensional conformal field theory in the the large central charge limit. This class of states includes the states created by the insertion of a finite number of local heavy operators. By using the monodromy analysis, we obtain the leading order entanglement entropy for the general state. We show that it is exactly captured by the Ryu-Takayanagi formula, by using the Wilsonian line prescription in the Chern-Simons formulation of the AdS$_3$ gravity.