Holographic entanglement entropy for a large class of states in 2D CFT

Bin Chen,Jie-Qiang Wu

doi:10.1007/jhep09(2016)015

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.

Highlights

1-loop level, the picture relies on the fact that the 1-loop partition function of any handlebody configuration [13, 14] could be reproduced by the CFT partition function [15]
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
We studied the entanglement entropy for a large class states in the 2D large c CFT

Summary

Entanglement entropy in a large class of states

The entanglement entropy is a measure of the entanglement between the subsystem and its complement. When we take the n → 1 limit to compute the entanglement entropy, the twist operator become a light operator. The entanglement entropy could be evaluated as the multi-point correlation function of the light operators. Let us consider the single interval case In this case we just need to consider the correlation function of two light operators. Taking the fusion of these two light operators, the correlation function can be expand into a series of the contributions from different conformal blocks. The conformal dimension of the operator φ satisfies 1 h c This condition means that we can make the saddle point approximation and ignore the back-reaction. Instead of directly solving the equation (2.28), we will use the holographic method to compute the two-point function and read the parameters γ1, γ2, and check that it satisfies the monodromy equation

Holographic computation via Wilson line

Wilson line prescription

Conclusion and discussion