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

TL;DR

This paper refines holographic entanglement entropy calculations for AdS solitons and black holes, revealing non-monotonic behavior, absence of topological entropy in certain cases, and proposing IR fixed-point states based on the AdS/MERA conjecture.

Contribution

It introduces a UV-independent renormalized entanglement entropy for AdS solitons and black holes, analyzing their phase transitions and fixed-point states with Gauss-Bonnet corrections.

Findings

Renormalized entanglement entropy is not always positive or monotonic.

No topological entanglement entropy for AdS_5 soliton with Gauss-Bonnet correction.

IR regime exhibits volume law for black holes, with smooth UV-IR crossover.

Abstract

We consider the refinement of the holographic entanglement entropy for the holographic dual theories to the AdS solitons and AdS black holes, including the corrected ones by the Gauss-Bonnet term. The refinement is obtained by extracting the UV-independent piece of the holographic entanglement entropy, the so-called renormalized entanglement entropy which is independent of the choices of UV cutoff. Our main results are (i) the renormalized entanglement entropies of the AdS$_{d+1}$ soliton for $d=4,5$ are neither monotonically decreasing along the RG flow nor positive definite, especially around the deconfinement/confinement phase transition; (ii) there is no topological entanglement entropy for AdS$_5$ soliton even with Gauss-Bonnet correction; (iii) for the AdS black holes, the renormalized entanglement entropy obeys an expected volume law at IR regime, and the transition between UV and IR regimes is a smooth crossover even with Gauss-Bonnet correction; (iv) based on AdS/MERA conjecture, we postulate that the IR fixed-point state for the non-extremal AdS soliton is a trivial product state.