Holographic entanglement beyond classical gravity

TL;DR

The paper analyzes holographic entanglement beyond classical gravity in AdS3/CFT2 by computing bulk one-loop corrections to entanglement and Rényi entropies. It uses Schottky uniformization to construct branched-cover geometries and Giombi–Yin determinants to evaluate quantum corrections, focusing on two setups: two intervals on a plane and a single interval on a torus. Analytic small-cross-ratio expansions, exact S_2 results, and numerical studies of higher Rényi entropies reveal universal bulk contributions missing at leading order, including mutual information for separated intervals, finite-size effects at high temperature, and entanglement asymmetry below the Hawking-Page transition. The results demonstrate how one-loop bulk effects encode information about entanglement structure and finite-size/temperature physics, offering concrete data points for quantum gravity in holographic settings. Overall, the work advances holographic entanglement by linking detailed bulk spectral data to boundary entanglement features beyond classical gravity."

Abstract

The Renyi entropies and entanglement entropy of 1+1 CFTs with gravity duals can be computed by explicit construction of the bulk spacetimes dual to branched covers of the boundary geometry. At the classical level in the bulk this has recently been shown to reproduce the conjectured Ryu-Takayanagi formula for the holographic entanglement entropy. We study the one-loop bulk corrections to this formula. The functional determinants in the bulk geometries are given by a sum over certain words of generators of the Schottky group of the branched cover. For the case of two disjoint intervals on a line we obtain analytic answers for the one-loop entanglement entropy in an expansion in small cross-ratio. These reproduce and go beyond anticipated universal terms that are not visible classically in the bulk. We also consider the case of a single interval on a circle at finite temperature. At high temperatures we show that the one-loop contributions introduce expected finite size corrections to the entanglement entropy that are not present classically. At low temperatures, the one-loop corrections capture the mixed nature of the density matrix, also not visible classically below the Hawking-Page temperature.

Figures (3)

• Figure 1: Some of the cycles in (\ref{['eq:othergen']}) generating the Schottky group for two choices of uniformization. In the top line the monodromy around the $[z_1,z_2]$ cycle has been trivialized and so the generators use the remaining $[z_2,z_3]$ cycle. In the second line the $[z_2,z_3]$ cycle has been trivialized and the generators use the remaining $[z_1,z_2]$ cycle.
• Figure 2: The mutual Rényi information $I_{n}^{(0)}$ of two disjoint intervals, at the classical level, plotted as functions of the cross-ratio $x$ for various $n$. The plot on the right is the same as the one on the left except that it is restricted to $x<1/2$, showing more clearly that the mutual Rényi informations with $n>1$ do not vanish for $x < 1/2$.
• Figure 3: (a) The one-loop contribution to the mutual Rényi information $I^{(1)}_{n}$ of two disjoint intervals plotted as functions of the cross-ratio $x$ for various $n$. The solid curves come from numerical calculations, and the dashed (or dotted) curves come from an analytic expansion in $x$ up to $x^8$ (or $x^7$) inclusive. (b) The same plot but now with $n=1$ black dashed/dotted curves from the analytic expansion.