# Refined Holographic Entanglement Entropy for the AdS Solitons and AdS black Holes

**Authors:** Masafumi Ishihara, Feng-Li Lin, Bo Ning  
**arXiv:** [1203.6153](https://arxiv.org/abs/1203.6153)  
**Date:** 2012-03-28  
**Summary page:** https://www.summarizepaper.com/en/paper/1203.6153v5/

## Key points

- Authors: Masafumi Ishihara, Feng-Li Lin, Bo Ning
- Focus: Holographic entanglement entropy in AdS solitons and AdS black holes
- Method: Incorporating corrections from Gauss-Bonnet term to refine understanding
- Renormalized entanglement entropies of AdS$_{d+1}$ solitons for $d=4,5$ not monotonically decreasing along RG flow near phase transition
- Absence of topological entanglement entropy for AdS$_5$ solitons even with Gauss-Bonnet corrections
- Renormalized entanglement entropy follows volume law in IR regime for AdS black holes
- Smooth crossover between UV and IR regimes observed with Gauss-Bonnet corrections
- Proposal that IR fixed-point state for non-extremal AdS solitons is a trivial product state based on AdS/MERA conjecture

## Summary

In their paper titled "Refined Holographic Entanglement Entropy for the AdS Solitons and AdS Black Holes," Masafumi Ishihara, Feng-Li Lin, and Bo Ning delve into the intricacies of holographic entanglement entropy within the framework of AdS solitons and AdS black holes. By incorporating corrections from the Gauss-Bonnet term, the authors aim to refine the understanding of this entropy measure by isolating the UV-independent component known as renormalized entanglement entropy. Their investigation yields several key findings. Firstly, they observe that the renormalized entanglement entropies of AdS$_{d+1}$ solitons for $d=4,5$ do not exhibit a monotonic decrease along the RG flow and lack positive definiteness in proximity to the deconfinement/confinement phase transition. Additionally, they highlight the absence of topological entanglement entropy for AdS$_5$ solitons even when considering Gauss-Bonnet corrections. Furthermore, their analysis extends to AdS black holes where they find that the renormalized entanglement entropy adheres to a volume law in the IR regime. Interestingly, they note a smooth crossover between UV and IR regimes even with Gauss-Bonnet corrections applied. Lastly, drawing on the AdS/MERA conjecture, they propose that the IR fixed-point state for non-extremal AdS solitons manifests as a trivial product state. Through their comprehensive exploration of holographic entanglement entropy in diverse gravitational backgrounds, Ishihara et al. contribute valuable insights into quantum information aspects of holography and offer new perspectives on emergent phenomena in gravitational systems.