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arXiv · 2309.03491

Holographic renormalized Entanglement and entropic $c-$function

Mitsutoshi Fujita·Song He·Yuan Sun·Jun Zhang
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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.

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Mitsutoshi Fujita, Song He, Yuan Sun, Jun Zhang. 2023-09-07. Holographic renormalized Entanglement and entropic $c-$function. https://arxiv.org/abs/2309.03491

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