Generalized entanglement entropy and holography

TL;DR

This paper introduces a generalized entanglement entropy based on a modified von Neumann entropy, explores its implications in holography, and finds significant corrections to the standard Ryu-Takayanagi formula in 2D CFTs and their gravity duals.

Contribution

It proposes a new entropy functional and extends the replica trick, analyzing its impact on gauge/gravity duality and entanglement entropy calculations.

Findings

New entropy correction terms larger than usual UV corrections

Modified Ryu-Takayanagi formula due to the generalized entropy

Significant deviations in entanglement entropy calculations in 2D CFTs

Abstract

In this work, we first introduce a generalized von Neumann entropy that depends only on the density matrix. This is based on a previous proposal by one of us modifying the Shannon entropy by considering non-equilibrium systems on stationary states, and an entropy functional depending only on the probability. We propose a generalization of the replica trick and find that the resulting modified von Neumann entropy is precisely the previous mentioned entropy that was obtained by other assumptions. Then, we address the question whether alternative entanglement entropies can play a role in the gauge/gravity duality. Our focus are 2d CFT and their gravity duals. Our results show corrections to the von Neumann entropy $S_0$ that are larger than the usual $UV$ ones and also than the corrections to the length dependent $AdS_3$ entropy which result comparable to the $UV$ ones. The correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT and the gravitational $AdS_3$ entropies.