Holographic renormalized Entanglement and entropic $c-$function

TL;DR

This paper calculates the holographic entanglement entropy and its renormalized form in AdS solitons, revealing universal features, phase transitions, and the effects of compactification across various dimensions.

Contribution

It introduces a method to compute cutoff-independent renormalized EE in AdS solitons and explores its behavior under dimensional reduction and phase transitions.

Findings

Renormalized EE is universal and cutoff-independent.

A quantum phase transition occurs at a critical subregion size.

Massive modes decouple at low energies, Wilson lines influence small-scale behavior.

Abstract

We compute holographic entanglement entropy (EE) and the renormalized EE in AdS solitons with gauge potential for various dimensions. The renormalized EE is a cutoff-independent universal component of EE. Via Kaluza-Klein compactification of $S^1$ and considering the low-energy regime, we deduce the $(d-1)$-dimensional renormalized EE from the odd-dimensional counterpart. This corresponds to the shrinking circle of AdS solitons, probed at large $l$. The minimal surface transitions from disk to cylinder dominance as $l$ increases. The quantum phase transition occurs at a critical subregion size, with renormalized EE showing non-monotonic behavior around this size. Across dimensions, massive modes decouple at lower energy, while degrees of freedom with Wilson lines contribute at smaller energy scales.