# A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections

## TL;DR

This paper employs geodesic Witten diagrams to analyze holographic entanglement entropy, establishing a duality with conformal blocks, and explores quantum corrections, bulk entanglement, and connections to entanglement of purification.

## Contribution

It introduces a geodesic Witten diagram framework for holographic entanglement entropy and elucidates quantum corrections and their relation to bulk entanglement and Renyi entropy.

## Key findings

- Agreement between Ryu-Takayanagi and identity block contributions.
- Quantum bulk corrections linked to bulk entanglement entropy.
- Correspondence between entanglement of purification and Renyi entropy corrections.

## Abstract

We use the formalism of geodesic Witten diagrams to study the holographic realization of the conformal block expansion for entanglement entropy of two disjoint intervals. The agreement between the Ryu-Takayanagi formula and the identity block contribution has a dual realization as the product of bulk to boundary propagators. Quantum bulk corrections instead arise from stripped higher order diagrams and back-reaction effects; these are also mapped to the structure for $G_N^0$ terms found in \cite{Faulkner:2013ana}, with the former identified as the bulk entanglement entropy across the Ryu-Takayanagi surfaces. An independent derivation of this last statement is provided by implementing a twist-line formalism in the bulk, and additional checks from the computation of mutual information and single interval entanglement entropy. Finally an interesting correspondence is found between the recently proposed holographic entanglement of purification, and an approximated form for certain $1/c$ Renyi entropies corrections.