Renormalized Entanglement Entropy for BPS Black Branes

TL;DR

This paper calculates the renormalized entanglement entropy for BPS black branes in 4d gauged supergravity, revealing a monotonic decrease followed by an increase, driven by the interplay of entanglement and mixedness.

Contribution

It introduces the computation of REE for BPS black branes and analyzes its behavior across different regimes, highlighting the competing effects of entanglement and mixedness.

Findings

REE decreases monotonically with entangling region size

REE reaches a minimum at a critical point

REE approaches the brane's entropy density in the IR

Abstract

We compute the renormalized entanglement entropy (REE) for BPS black solutions in ${\cal N}=2$, 4d gauged supergravity. We find that this quantity decreases monotonically with the size of the entangling region until it reaches a critical point, then increases and approaches the entropy density of the brane. This behavior can be understood as a consequence of the REE being driven by two competing factors, namely entanglement and the mixedness of the black brane. In the UV entanglement dominates, whereas in the IR the mixedness takes over.